Susan Carroll, a senior scholar at the Center for American Women and Politics, a nonpartisan research organization in New Jersey, agreed, adding that she’s seen no consistent polling to suggest that Obama is losing his edge among women.

“I think there was erosion in women’s support following the first debate and movement toward Romney, but I think it happened for men as well,” Carroll said. “But at this point there’s no evidence that it’s continuing, that Romney is continuing to pick up women voters.”

She said Obama’s focus on women stems from the fact that there are slightly disproportionately more women among voters who have yet to make up their minds, and women make up a critical part of Obama’s base.

“This campaign is going to come down to turnout,” she said. “You would expect him to be out there speaking to women and mobilizing his base.”

Still, there are voters like Carrie Williams, 33, a Virginia resident who works in marketing and advertising, and should be in Obama’s camp. Although she didn’t vote in 2008, she comes from a Democratic family and had rooted for Obama to succeed.

The debates, however, made up her mind. She’ll be voting for Romney. Of Obama, she says, “I just don’t think he’s giving us any indication that he has a plan for the future.”

But Lily Bryan, 24, a Virginia resident who voted for Obama in 2008, will do so again. She acknowledges some in her circle “have become a little disenchanted,” but will still support Obama.

“It’s mostly a lot of social issues,” she said, listing abortion rights, equal pay for women and gay marriage as issues where she agrees with Obama.

Any softening of female support comes as Obama faces a significant gap with males, especially white men.

Tom Edmonds, a Republican political consultant in Virginia, says Obama’s approach to women voters – including an emphasis on access to birth control and abortion rights -- may be misplaced during an economic downturn and is doing little to bring aboard male voters.

“Obama is trying to appeal to women on one single point and they want a job, economic opportunities,” Edmonds said. “They want the same things men want. Obama’s trying to appeal to women through the abortion issue almost exclusively while Romney is trying to appeal to them on jobs and the economy. As Romney’s stock has gone up with men, it’s also gone up with women."

Obama’s approach has its fans: as the president walked into The Common Man restaurant in Merrimack, N.H., on Saturday after a campaign appearance in nearby Nashua, a woman sitting with her husband and two children grabbed Obama’s arm.

“I’m so happy with your support of women,” she told the president.

Obama replied: "Women are always – usually -- ahead of the game.”