As John Kerry and Ronald Reagan can attest to, debates can move the polls and influence the narrative of the horse race. But despite movement in the direction of the challenger, there's not much evidence that the debates have ever fundamentally reshaped a race.
Yes, debates do seem to help the challenging party candidate. The most prominent two examples might be Reagan (in 1980) and Kerry, who were both challenging party candidates who fell from previous heights following the in-party convention. In each instance, their opponents did not reclaim their old supporters, suggesting that a disproportionate share of undecided voters were latent supporters of the challenging candidate. For instance, Kerry fell from 48 percent after the DNC to a low of 42.5 percent after the RNC, but Bush only peaked at about 50 percent of the vote following his own convention, suggesting that he hadn’t persuaded many of the former Kerry supporters to join his cause. In 1980, Reagan reached the upper forties following the RNC and fell to the low forties following the DNC. But once again, Carter never jumped far from 40 percent of the vote, suggesting that he hadn’t made inroads among latent Reagan voters.
In the aftermath of the 1980 and 2004 presidential debates, strong performances by Reagan and Kerry allowed both candidates to recapture many of their latent supporters. Perhaps many of these undecided voters genuinely could have voted for either side. But the fact that they previously supported the challenging party candidate, generally disapproved of the president’s performance, and weren’t swayed by the in-party convention suggests that these voters were likely to break toward the challenger, even without a solid debate performance.
Additionally, notice that neither Kerry, nor Reagan appeared to persuade voters who had already committed to the other candidate. Carter held about 40 percent of the vote heading into the debates; he would ultimately win 41 percent of the vote. Bush held about 49 percent of the vote heading into the debates and he took 51 percent on Election Day. Neither Reagan nor Kerry secured a large enough share of the vote to indicate that they actually attracted true converts; Kerry only reached 46 or 47 percent following the debates and Reagan only moved to the mid-to-upper forties in pre-election polls.
What would a similar movement toward Romney look like in 2012? Unlike in Reagan's case, the return of latent Romney supporters won't give him the lead. 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.
Obama's lead is relatively modest, especially for an incumbent president on pace for reelection. But no candidate has trailed by as much as Romney heading into the first debate and gone on to win the election. That doesn't mean it can't happen, but perhaps it's not especially likely if it hasn't happened before.