The campaigns of President Barack Obama and GOP presidential nominee Gov. Mitt Romney both released ads Thursday on taxes.

The Romney campaign struck first, with "Who Will Raise Taxes?," a new ad in which a narrator says, "According to an independent, non-partisan study, Barack Obama and the liberals will raise taxes on the middle class by $4,000." But the study the ad refers to is the American Enterprise Institute, a conservative think-tank analyzing the costs of debt servicing.

The Obama campaign's ad highlights Romney saying at Wednesday's debate, "I’m not in favor of a $5 trillion tax cut. That’s not my plan." Says a narrator, "If we can’t trust him here … How could we ever trust him here [showing the Oval Office]?" The spot is airing in Colorado, Florida, Iowa, New Hampshire, Nevada, Ohio and Virginia.

In the debate, Romney said, "I'm not asking for a $5 trillion tax cut. What I've said is I won't put in place a tax cut that adds to the deficit. ... I've got five boys. I'm used to people saying something that's not always true, but just keep on repeating it and ultimately hoping I'll believe it."

But Romney's tax plan costs about $5 trillion, according to the nonpartisan Tax Policy Center. If Romney doesn't want his plan to cost $5 trillion, it likely means he won't be able to reduce rates by 20 percent across-the-board.

He has also said that he will not eliminate popular tax deductions such as mortgage interest, charitable contributions and health care, but the Tax Policy Center said he would have to eliminate middle-class deductions if he wanted to cut rates and maintain revenue-neutrality.

Also on HuffPost:

Loading Slideshow...
  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) greets Republican presidential candidate Mitt Romney (L) following the first presidential debate at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney went head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) greets Republican presidential candidate Mitt Romney (L) following the first presidential debate at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney went head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) greets Republican presidential candidate Mitt Romney (L) following the first presidential debate at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney went head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (L) and Republican presidential candidate Mitt Romney finish their debate at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • Republican presidential nominee Mitt Romney, left, shakes hands with President Barack Obama following the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • President Barack Obama shakes hands with Republican presidential nominee Mitt Romney after the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool-Michael Reynolds)

  • President Barack Obama hugs First lady Michelle Obama after the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool-Michael Reynolds)

  • Republican presidential nominee Mitt Romney, left, and President Barack Obama speak after the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • Mitt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney talk at the end of the first presidential debate in Denver, Wednesday, Oct. 3, 2012. (AP Photo/Charles Dharapak)

  • Mitt Romney, Barack Obama

    Republican presidential nominee Mitt Romney and President Barack Obama laugh after the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • President Barack Obama and Republican presidential nominee Mitt Romney participate in shakes hands with Ann Romney after the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool-Michael Reynolds)

  • Republican presidential nominee Mitt Romney and family talk to President Barack Obama and family after the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool, Rick Wilking)

  • Left, President Barack Obama hugs his wife Michelle with Republican presidential nominee Mitt Romney hugs his wife Ann following the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • President Barack Obama hugs his wife Michelle following the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/David Goldman)

  • Mitt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney talk at the end of the first presidential debate in Denver, Wednesday, Oct. 3, 2012. (AP Photo/Charles Dharapak)

  • Mitt Romney

    Republican presidential nominee Mitt Romney answers a question during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • Barack Obama

    President Barack Obama gestures during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • Mitt Romney

    Republican presidential nominee Mitt Romney gestures during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • Mitt Romney

    Republican presidential nominee Mitt Romney smiles as President Barack Obama during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • President Barack Obama smiles at moderator Jim Lehrer during the first presidential debate with Republican presidential nominee Mitt Romney at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • Republican presidential nominee Mitt Romney speaks during the first presidential debate with President Barack Obama at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • President Barack Obama points to Republican presidential nominee Mitt Romney during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • President Barack Obama answers a question of moderator Jim Lehrer during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool-Michael Reynolds)

  • Barack Obama

    President Barack Obama smiles as Republican presidential nominee Mitt Romney answers a question during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • President Barack Obama, right, listens to Republican presidential nominee Mitt Romney during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/David Goldman)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and republican Presidential candidate Mitt Romney (L) participate in the first presidential debate at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012, moderated by Jim Lehrer (C) of the PBS NewsHour. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    Republican presidential candidate Mitt Romney (L) speaks during the first presidential debate with US President Barack Obama October 3, 2012 at the University of Denver in Denver, Colorado. AFP PHOTO/Mandel NGAN (Photo credit should read MANDEL NGAN/AFP/GettyImages)

  • Mitt Romney, Barack Obama

    President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate the first presidential debate in Denver, Wednesday, Oct. 3, 2012. (AP Photo/Charles Dharapak)

  • Republican presidential nominee Mitt Romney's shadow is reflected during the first presidential debate President Barack Obama withat the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/David Goldman)

  • President Barack Obama speaks during the first presidential debate with Republican presidential nominee Mitt Romney at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • US-VOTE-2012-DEBATE

    US President Barack Obama listens during his debate with Republican presidential candidate Mitt Romney at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Nicholas KAMM (Photo credit should read NICHOLAS KAMM/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    US President Barack Obama debates Republican presidential candidate Mitt Romney at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    Republican presidential candidate Mitt Romney speaks during his debate with US President Barack Obama at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    US President Barack Obama (R) and Republican presidential candidate Mitt Romney (L) participate in the first presidential debate at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012, moderated by Jim Lehrer (C) of the PBS NewsHour. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • Barack Obama, Mitt Romney

    Republican presidential candidate, former Massachusetts Gov. Mitt Romney, left, and President Barack Obama, right, speak during their first debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pablo Martinez Monsivais)

  • Mitt Romney, Barack Obama

    President Barack Obama answers a question as Republican presidential nominee Mitt Romney listens during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Charlie Neibergall)

  • President Barack Obama listens as Republican presidential nominee Mitt Romney answers a question during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Rick Wilking, Pool)

  • Obama And Romney Square Off In First Presidential Debate In Denver

    DENVER, CO - OCTOBER 03: U.S. President Barack Obama (L) listens as Republican presidential candidate and former Massachusetts Gov. Mitt Romney (R) speaks during the Presidential Debate at the University of Denver on October 3, 2012 in Denver, Colorado. The first of four debates for the 2012 Election, three Presidential and one Vice Presidential, is moderated by PBS's Jim Lehrer and focuses on domestic issues: the economy, health care, and the role of government. (Photo by Michael Reynolds-Pool/Getty Images)

  • Obama And Romney Square Off In First Presidential Debate In Denver

    DENVER, CO - OCTOBER 03: Democratic presidential candidate, U.S. President Barack Obama (R) speaks as Republican presidential candidate, former Massachusetts Gov. Mitt Romney listens during the Presidential Debate at the University of Denver on October 3, 2012 in Denver, Colorado. The first of four debates for the 2012 Election, three Presidential and one Vice Presidential, is moderated by PBS's Jim Lehrer and focuses on domestic issues: the economy, health care, and the role of government. (Photo by Doug Pensinger/Getty Images)

  • Obama And Romney Square Off In First Presidential Debate In Denver

    DENVER, CO - OCTOBER 03: Republican presidential candidate, former Massachusetts Gov. Mitt Romney (L) speaks as Democratic presidential candidate, U.S. President Barack Obama (R) listens during the Presidential Debate at the University of Denver on October 3, 2012 in Denver, Colorado. The first of four debates for the 2012 Election, three Presidential and one Vice Presidential, is moderated by PBS's Jim Lehrer and focuses on domestic issues: the economy, health care, and the role of government. (Photo by Doug Pensinger/Getty Images)

  • US-VOTE-2012-DEBATE

    US President Barack Obama listens during his debate with Republican Presidential candidate Mitt Romney at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Nicholas KAMM (Photo credit should read NICHOLAS KAMM/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    The shadow of Republican Presidential candidate Mitt Romney is projected beneath a copy of The Declaration of Independence during the presidential debate with US President Barack Obama at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    Republican presidential candidate Mitt Romney participates in the first presidential debate with US President Barack Obama at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012, moderated by Jim Lehrer of the PBS NewsHour. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)

  • President Barack Obama answers a question during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool-Michael Reynolds)

  • Republican presidential nominee Mitt Romney speaks during the first presidential debate with President Barack Obama at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/David Goldman)

  • Republican presidential nominee Mitt Romney, left, listens to President Barack Obama during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Eric Gay)

  • President Barack Obama watches as Republican presidential nominee Mitt Romney answers a question during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool, Rick Wilking)

  • Republican presidential nominee Mitt Romney points to President Barack Obama during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/David Goldman)

  • US-VOTE-2012-DEBATE

    US President Barack Obama speaks during his debate with Republican Presidential candidate Mitt Romney at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Nicholas KAMM (Photo credit should read NICHOLAS KAMM/AFP/GettyImages)

  • US-VOTE-2012-DEBATE

    US President Barack Obama speaks during his debate with Republican Presidential candidate Mitt Romney at Magness Arena at the University of Denver in Denver, Colorado, October 3, 2012. After hundreds of campaign stops, $500 million in mostly negative ads and countless tit-for-tat attacks, Obama and Romney go head-to-head in their debut debate. AFP PHOTO / Nicholas KAMM (Photo credit should read NICHOLAS KAMM/AFP/GettyImages)

  • Republican presidential nominee Mitt Romney answers a question during the first presidential debate at the University of Denver, Wednesday, Oct. 3, 2012, in Denver. (AP Photo/Pool-Michael Reynolds)