That's the key question, right? So here are some of the more thoughtful estimates from the election wonks.
John Sides: "Let’s assume that the same fraction of undecided voters shift in Romney’s direction as shifted in Bush’s direction. In 2000, that was 25 percent of undecideds (3/12=.25). In 2012, the proportion of undecideds is about 5 percent. So 25 percent of 5 percent is 1.25 points—about what I predicted last night. It could end up being a bit more, if you think that Obama has been out-performing the fundamentals of the race, and thus we were due for a course correction."
Nate Silver: "It seems likely that Mr. Romney will make at least some gains in head-to-head polls after the debate, and entirely plausible that they will be toward the high end of the historical range, in which polls moved by about three percentage points toward the candidate who was thought to have the stronger debate."
Nate Cohn: "Regardless of whether Romney has upended the race, he can expect something of a bounce in the post-debate polls. Following the first debate in 2004, Kerry closed to within 1.6 points in the RCP average, compared to his final 2.4-point defeat. Four years earlier still, Bush seized the lead in post-debate polls and didn’t relinquish it until the Election Day results showed Gore winning the popular vote...the key questions are whether Obama falls far beneath 49 percent and whether Romney can get past 47. If neither of these conditions are met, then Romney's performance just wasn't good enough."
It's also worth remembering what political scientists Robert Erikson and Chistopher Wlezien found after reviewing every public poll taken before and after every televised debate: "the best prediction from the debates is the initial verdict before the debates."
Overall, I'd expect the polls to tighten, perhaps even substantially. But how much they tighten will be very telling. Wednesday was as good a night as Romney can expect to have in the rest of this campaign, in front of as big an audience as he'll get, with a maximum of media coverage. So his bounce will help tell us how many voters really remain persuadable, or at least how many of the persuadable voters are paying attention to the final events of the campaign. If that number is high, Romney should close the gap substantially, if not pull slightly ahead. If it's low, he won't see much bounce, and it will be that much harder to see his path to victory.
Think about the people you know: How many of the Obama voters who thought Romney won the debate seem ready to change their vote today? Personally, I don't know any Obama voters who thought he won the debate. But I also don't know any Obama voters who have said they're now supporting Romney. Now, my circles are unusually politically active, and so their preferences are unusually hard to move. But remember that the most persuadable voters pay the least attention to politics, so they may not know or care that Obama lost a debate. The polls, in other words, will quickly tell us whether Obama simply looked bad or whether he lost real support.
The second question, of course, will be whether the bounce persists. This is the first of three presidential debates. It's possible all of them will be lopsided victories for Romney, but unlikely. The expectations game now is such that Obama won't have to do that much better, and Romney won't have to do that much worse, for Obama's next performance to be graded more favorably. That's basically what happened with the Bush-Kerry debates in 2004, and it helped Bush recover after his weak initial performance. So just as with the conventions, keep in mind that it will be very hard to say what effect "the debates" had until they're actually over.