Mitt Romney's up by 1 nationally, but trails by 4 in a dozen key battleground states, according to a new NPR Battleground poll released Tuesday.
The poll also shows that the first debate between Romney and President Barack Obama reshaped the race.
Romney's support among independents grew after that debate; in 2008, Obama won among independents.
"So were it not for the debates," said Republican pollster Whit Ayres, who conducted the poll along with Democratic pollster Stan Greenberg, "I think Obama would be cruising to a victory right now. Because of the debates, this is going to be an incredibly close election."
The poll found one-third saying the debates made them more likely than they had been to vote for Romney, while 28 percent said the debates made them more likely to vote for the president.
Greenberg, though, felt good about Obama's chances, since he led by 4 in states likely to decide the race: Nevada, Colorado, New Mexico, Iowa, Wisconsin, Michigan, Ohio, Pennsylvania, New Hampshire, Virginia, North Carolina and Florida. Both the Romney lead and the Obama lead were within the poll's margin of error.
The pollsters surveyed 1,000 likely voters from Oct. 23-25. Margin of error for such a poll is 3 percentage points for the national sample and 4.5 percentage points for the smaller sub-sample in the battleground states.