WASHINGTON (AP) ― President Barack Obama and Republican Mitt Romney vied aggressively for the support of female voters, accusing each other of failing America’s women as they fought to keep up the momentum after their contentious, finger-pointing debate.

At issue Wednesday was the candidates’ approach to gender pay equity laws and Romney’s comment during the debate that he was sent “binders full of women” when he was governor of Massachusetts.

Romney made the remark while recalling that he looked to women’s organizations after being dissatisfied with the mostly male applicants for senior level positions in his administration. But it set off a storm of media parodies, and Obama jumped on the comment to try to portray Romney as out of step with the concerns of women.

“We don’t have to collect a bunch of binders to find qualified, talented, driven young women,” Obama said at a rally in Mount Vernon, Iowa.

There was little mystery in the candidates’ focus on women. An AP-GfK survey taken in mid-September, when Obama was leading in the opinion polls, found that 8 percent of all likely votes were women who were either undecided or said they might change their minds. 

Polls since the first debate two weeks ago, when Obama fared poorly, show gains for Romney among women voters. That’s a shift the Democratic president can ill afford given the traditional Republican advantage among men. But Obama’s Tuesday night debate performance was much stronger than the first time around, and he was staying on the attack on the campaign trail Wednesday.

Not even Republicans disputed that Obama’s debate performance was much improved from the listless showing two weeks earlier that helped spark a rise in the polls for Romney. But the first post-debate polls were divided, some saying Romney won, others finding Obama did.

The two rivals meet one more time, next Monday in Florida.

Democrats rebutted Romney’s memory of the binders he received as the newly elected governor of Massachusetts in 2002.

On a conference call arranged by the Democratic National Committee, a former executive director of the Massachusetts Government Appointments Project said the group provided the resumes of women qualified for appointment unprompted. “To be perfectly clear, Mitt Romney did not request” them, said Jesse Mermell.

Vice President Joe Biden, campaigning in battleground Colorado, mocked Romney on the same topic but in terms more pungent than Obama’s. “What I can’t understand is how he’s gotten into this sort of 1950s time warp in terms of women,” Biden said. “The idea he had to go and ask where a qualified woman was. He just should have come to my house. He didn’t need a binder.”

Romney quickly countered with a combination testimonial and fundraising appeal from Kerry Healey, who was his lieutenant governor in Massachusetts. She said he had named numerous women to his administration, adding, “He sought out our counsel, and he listened to our advice. We didn’t always agree, but we were always respected.”

Obama wore a pink wristband to show support for Breast Cancer Awareness Month as he campaigned in Iowa and then Ohio, and reminded his audience that the first legislation he signed after becoming president made it easier for women to take pay grievances to court.

Romney took no position on that bill when it passed Congress, and his campaign says he would not seek its repeal. But Obama chided him, saying, “That shouldn’t be a complicated question. Equal pay for equal work.”

Romney’s campaign launched a new television commercial that seemed designed to take the edge ever so slightly off his opposition to abortion ― the latest example of his recent move toward the middle ― while urging women voters to keep pocketbook issues uppermost in their minds when they cast their ballots.

“In fact he thinks abortion should be an option in cases of rape, incest or to save a mother’s life,” says a woman in the new ad. Pivoting quickly to economic matters, she adds, “But I’m more concerned about the debt our children will be left with. I voted for President Obama last time, but we just can’t afford four more years.”

That dovetailed with Romney’s personal pitch to an audience in Virginia.

“This president has failed American’s women. They’ve suffered in terms of getting jobs,” he declared, saying that 3.6 million more of them are in poverty now than when Obama took office.

His running mate, Republican Rep. Paul Ryan, echoed that message in Ohio.

“Twenty-six million women are trapped in poverty today. That’s the highest rate in 17 years,” he said. “We need to get people back to work.”

With recent gains in the polls for Romney, he and the president are locked in an exceedingly close race as they shuttle from one critical state to another and dispatch surrogates ranging from former President Bill Clinton to ex-Secretary of State Condoleezza Rice to locations they cannot make on their own.

Obama spoke to a crowd of about 14,000 students and supporters at Ohio University, imploring them to vote early. “I want your vote. I am not too proud to beg. I want you to vote,” he said.

States where voters are neither reliably Democratic nor Republican take on added importance in U.S. presidential elections because the outcome is not decided by the nationwide popular vote. Instead, candidates compete for each state’s electoral votes. Each state gets one electoral vote for each of its Congress members.

A little less than three weeks before Election Day, Obama appears on course to win states and the District of Columbia that account for 237 of the 270 electoral votes needed for victory. The same is true for Romney in states with 191 electoral votes.

The remaining 110 electoral votes are divided among the hotly contested battleground states of Florida (29), North Carolina (15), Virginia (13), New Hampshire (4), Iowa (6), Colorado (9), Nevada (6), Ohio (18) and Wisconsin (10).