By NANCY BENAC, ASSOCIATED PRESS

WASHINGTON — Still neck-and-neck after all these months, Barack Obama and Mitt Romney head into their third and final debate with each man eager to project an aura of personal strength and leadership while raising doubts about the steadiness and foreign policy credentials of the other guy.

Each is aiming for a commanding performance Monday to settle the seesaw dynamics of the first two debates: Romney gave Obama an old-fashioned shellacking in the first round, and the chastened president rebounded in their second encounter.

The 90-minute faceoff at Lynn University in Boca Raton, Fla., offers the candidates their last opportunity to stand one-on-one before tens of millions of Americans and command their undivided attention before next month's election. Both candidates largely dropped out of sight and devoted their weekends to debate preparations, a sure sign of the high importance they attach to the event.

While the principals warm up for their evening debate in the battleground state of Florida, their running mates will be busy Monday seeking votes in two of the eight other states whose up-for-grabs electoral votes will determine the next president – Vice President Joe Biden in Ohio and Republican Rep. Paul Ryan in Colorado. Also still hotly contested: Iowa, New Hampshire, Nevada, North Carolina, Wisconsin and Virginia.

It fell to campaign surrogates on Sunday talk shows to frame the foreign policy matters that moderator Bob Schieffer will put before the candidates in a discussion sure to reflect "how dangerous the world is in which we live," as the CBS newsman put it. Iran's nuclear intentions, the bloody crackdown in Syria, economic angst in Europe, security concerns in Afghanistan, China's growing power – all that and more are on the agenda.

And all feed into the broader debate over which candidate offers the steady hand and sound judgment for a nation facing myriad challenges at home and abroad.

Florida Sen. Marco Rubio, arguing for the Republicans, faulted Obama for "his failure to outline broad goals, real goals, a real view of what America's role in the world should be." Romney, by contrast, would "use America's role in the world as a catalyst for peace, prosperity and freedom," he said.

Ryan, campaigning in Colorado Springs, Colo., on Sunday, faulted the president for potential defense cuts and said that when adversaries "see us projecting weakness, when they see us hollowing out our military ... they think we are a superpower in decline." It was a likely preview of one of Romney's arguments in the debate.

Obama adviser David Axelrod said that when the president took office "we were isolated in our position on Iran and in the world. And today, the world is unified against Iran with us, all because of the leadership of this president."

The Obama campaign released a blistering memo from Senate Foreign Relations Committee Chairman John Kerry, D-Mass., accusing Romney of offering nothing but "endless bluster" on international issues.

"He is an extreme and expedient candidate who lacks the judgment and vision so vital for the Oval Office," said Kerry, who is considered a leading candidate to succeed Hillary Rodham Clinton as secretary of state if Obama wins a second term.

When it comes to their foreign policy credentials, both candidates have reasons for optimism and concern: While foreign policy has been a strength of Obama throughout the campaign, some recent polls show his advantage narrowing. The Pew Research Center's October poll, for example, found that 47 percent of Americans favored Obama to make "wise decisions about foreign policy," while 43 percent preferred Romney.

American University professor Jordan Tama said the difficult trick for Romney in the debate will be to challenge Obama on foreign policy without looking like he's criticizing the commander in chief, which can be off-putting to voters. Obama, for his part, must make the case that his policies are sound and his leadership strong despite ongoing challenges around the world, including unrest in the Middle East and the chaotic situation in Libya that left four Americans dead.

While foreign policy has been overshadowed during this campaign by concerns about the domestic economy and jobs at home, everything matters in a race this tight. A Wall Street Journal/NBC News poll released Sunday showed each candidate favored by 47 percent of likely voters, reflecting a boost of support for Romney following his strong performance in the first debate in early October.

With early voting under way in many states, there is precious little time for the candidates to break loose. More than 4 million Americans already have voted.

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  • US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate in the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • Republican presidential nominee Mitt Romney, left, addresses President Barack Obama during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Shannon Stapleton)

  • President Barack Obama, left, speaks to Republican presidential nominee Mitt Romney during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Win McNamee)

  • Republican presidential nominee Mitt Romney and President Barack Obama speak during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/David Goldman)

  • President Barack Obama and Republican presidential nominee Mitt Romney speak during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/David Goldman)

  • HEMPSTEAD, NY - OCTOBER 16: Republican presidential candidate Mitt Romney (L) speaks as U.S. President Barack Obama (R) listens during a town hall style debate at Hofstra University October 16, 2012 in Hempstead, New York. During the second of three presidential debates, the candidates fielded questions from audience members on a wide variety of issues. (Photo by Shannon Stapleton-Pool/Getty Images)

  • US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • Republican Presidential nominee Mitt Romney (rear) and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • Republican Presidential nominee Mitt Romney (L) and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US President Barack Obama and Republican presidential candidate Mitt Romney both speak at the same time during the second presidential debate October 16, 2012 at the David Mack Center at Hofstra University in Hempstead, New York. AFP PHOTO/Mandel NGAN (Photo credit should read MANDEL NGAN/AFP/Getty Images)

  • US President Barack Obama and Republican Presidential nominee Mitt Romney debate on October 16, 2012 at Hofstra University in Hempstead, New York. Undecided voters asked questions during a town hall format. AFP PHOTO/Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

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  • US-VOTE-2012-DEBATE

    US President Barack Obama (L) Republican presidential candidate Mitt Romney (R) participate in the second presidential debate at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • Mitt Romney, Barack Obama

    Republican presidential nominee Mitt Romney and President Barack Obama shake hands after the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Charlie Neibergall)

  • Mitt Romney, Barack Obama

    Republican presidential nominee Mitt Romney and President Barack Obama shake hands after the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Charlie Neibergall)

  • President Barack Obama shakes hands with Republican presidential nominee Mitt Romney at the end of the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/David Goldman)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (L) and Republican presidential candidate Mitt Romney (R) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • MItt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney speak during the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • MItt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate in the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (L) and Republican presidential candidate Mitt Romney (R) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • Republican presidential nominee Mitt Romney listens as President Barack Obama speaks during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/David Goldman)

  • Republican presidential nominee Mitt Romney and President Barack Obama speak during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/David Goldman)

  • Barack Obama, Mitt Romney

    President Barack Obama, right, listens as Republican presidential candidate former Massachusetts Gov. Mitt Romney answers a question from a member of the audience during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012 in Hempstead, N.Y. (AP Photo/Mary Altaffer)

  • MItt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate in the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • President Barack Obama and Republican presidential nominee Mitt Romney speak during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/David Goldman)

  • MItt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate in the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • Mitt Romney, Barack Obama

    Republican presidential nominee Mitt Romney and President Barack Obama spar during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Charlie Neibergall)

  • President Barack Obama, left, and Republican presidential nominee Mitt Romney address members of the audience during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Michael Reynolds)

  • US-VOTE-2012-DEBATE

    US President Barack Obama and Republican presidential candidate Mitt Romney both speak at the same time during the second presidential debate October 16, 2012 at the David Mack Center at Hofstra University in Hempstead, New York. AFP PHOTO/Mandel NGAN (Photo credit should read MANDEL NGAN/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    CNN's Candy Crowley (C) conducts the second presidential debate with US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • MItt Romney, Barack Obama

    President Barack Obama speaks as Republican presidential candidate and former Massachusetts Gov. Mitt Romney listens during the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • President Barack Obama listens as Republican presidential nominee Mitt Romney speaks during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Eric Gay)

  • Mitt Romney, Barack Obama

    Republican presidential nominee Mitt Romney and and President Barack Obama answer a question during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Charlie Neibergall)

  • President Barack Obama addresses members of the audience during the second presidential debate with Republican presidential nominee Mitt Romney at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Shannon Stapleton)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • MItt Romney, Barack Obama

    President Barack Obama speaks as Republican presidential candidate and former Massachusetts Gov. Mitt Romney listens during the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • A member of the audience asks President Barack Obama a question during the second presidential debate with Republican presidential nominee Mitt Romney at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Win McNamee)

  • President Barack Obama, left, speaks to Republican presidential nominee Mitt Romney during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Win McNamee)

  • US-VOTE-2012-DEBATE

    Republican Presidential nominee Mitt Romney and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • Moderator Candy Crowley, center, addresses President Barack Obama, left, and Republican presidential nominee Mitt Romney during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Michael Reynolds)

  • US-VOTE-2012-DEBATE

    Republican Presidential nominee Mitt Romney (L) and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    Republican Presidential nominee Mitt Romney and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • Republican presidential nominee Mitt Romney and President Barack Obama speak during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Eric Gay)

  • Barack Obama, Mitt Romney

    Republican presidential nominee Mitt Romney answers a question as President Barack Obama listens during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool, Rick Wilking)

  • Republican presidential nominee Mitt Romney, left, addresses President Barack Obama during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Shannon Stapleton)

  • Republican presidential nominee Mitt Romney listens as President Barack Obama speaks during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Eric Gay)

  • President Barack Obama addresses members of the audience during the second presidential debate with Republican presidential nominee Mitt Romney at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Shannon Stapleton)

  • US-VOTE-2012-DEBATE

    Republican Presidential nominee Mitt Romney (rear) and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican Presidential candidate Mitt Romney argue during the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)

  • MItt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate in the second presidential debate at Hofstra University in Hempstead, N.Y., Tuesday, Oct. 16, 2012. (AP Photo/Charles Dharapak)

  • Republican presidential nominee Mitt Romney, left, listens as President Barack Obama addresses members of the audience during the second presidential debate at Hofstra University, Tuesday, Oct. 16, 2012, in Hempstead, N.Y. (AP Photo/Pool-Michael Reynolds)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican Presidential candidate Mitt Romney argue during the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / TIMOTHY CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    Republican Presidential nominee Mitt Romney (L) listens to US President Barack Obama on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the second presidential debate, the only held in a townhall format, at the David Mack Center at Hofstra University in Hempstead, New York, October 16, 2012, moderated by CNN's Candy Crowley. AFP PHOTO / Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

  • US-VOTE-2012-DEBATE

    Republican Presidential nominee Mitt Romney (L) and US President Barack Obama debate on October 16, 2012 during the second of three presidential debates at Hofstra University in Hempstead, New York. AFP PHOTO / TIMOTHY A. CLARY (Photo credit should read TIMOTHY A. CLARY/AFP/Getty Images)