"I heard him go out of his way to sound so moderate during the debate," she said. "And I thought: 'Who is this? Where did this come from?' He may sound like he's focused on the middle class. But where's the record?"
Obama, meanwhile, has been working to shore up his support among men, who tend to be more Republican than women. In the 2008 election, men broke 49 percent for Obama to 48 percent for John McCain, even though Obama got 53 percent of the vote overall. The president's job approval ratings among men have tended to fall below his ratings among women throughout his first term.
A month ago, Romney's advantage among men was 13 percentage points. Now, it's down to 5 points, with most of the shift toward Obama coming among unmarried men.
Obama's election chances hinge on turning out voters like Jon Gerton, a disabled construction worker from Jonesboro, Ark. Gerton's a staunch Obama supporter — but he didn't vote in 2008.
"It takes longer than four years to get things to the point where things are going better," Gerton said. "Four years, it's not very long."
There has been a gender gap in every presidential election since 1980. In 2008, women were 7 percentage points more likely than men to vote for Obama.
Overall, people are significantly more optimistic about the economy and unemployment in the coming year than they have been at any point in AP-GfK polling going back to March 2011, when the poll first started asking those questions. And likely voters are even more optimistic than other adults.
Nearly six in 10 likely voters think the economy will improve in the next year, up from 46 percent last month. And 42 percent think the number of unemployed Americans will drop in the next year, up from 32 percent in September.