Unless you're David Plouffe or another member of President Barack Obama's cheerleading squad, you probably wouldn't argue that Obama won Wednesday night's debate. Indeed, instant polls from CNN and CBS showed Romney leading Obama by 42 to 22 percentage points, respectively, on the question of who won.

But can even a dominant win in a debate produce a victory in November? A few key numbers suggest that Romney supporters shouldn't expect too much as a result of last night's performance.

One of those numbers is 32. That's the percentage of undecided voters who told Washington Post and ABC News pollsters last week that they were "very interested" in the presidential debates. By contrast, 59 percent of definite Obama supporters and 53 percent of Romney supporters said they were "very interested."

As Scott Clement wrote for The Fix, "The poll’s finding underscores the challenge for Obama and Romney to sway a shrinking and elusive slice of the electorate with less than five weeks left in the contest. In addition to lacking clear support for Obama or Romney, on-the-fence voters are much less likely to say they are 'absolutely certain to vote' than those with firm opinions, even further limiting their potential impact on the election."

The narrowness and elusiveness of that slice of the electorate may explain why John Kerry's acclaimed performance in the 2004 presidential debates didn't lead to a Kerry presidency. Although Kerry gained about four points in the polls between the end of the Republican National Convention and the end of the debates, that only put him at 46 or 47 percentage points overall -- less than the 48 points that pollsters gave him at his peak in the days leading up to the convention.

In other words, it's reasonable to conclude that the debates helped Kerry earn back the votes of disaffected voters who'd previously supported him, but he didn’t appear to win over many new converts.

Romney's performance could have a similar effect on voters and donors who were losing faith in his candidacy, and that makes things much more difficult for Obama. But unless he wins the votes of either Obama's supporters or those hard-to-reach undecided voters, he'll have a hard time winning in November. Nate Cohn of The New Republic explained it this way:

To date, Romney hasn't exceeded 47 percent of the vote, and a return to that number would not give him the lead, at least without a decrease in Obama's support. Although it's possible that Romney could convince Obama supporters to join his cause, it would probably be the first instance of the debates breaking out of the prior contours of the race.
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  • 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)