MOUNT VERNON, Iowa (AP) — One day after their contentious, finger-pointing debate, President Barack Obama and Republican Mitt Romney vied aggressively for the support of women voters Wednesday, as they and their running mates charged across nearly a half-dozen battleground states in the close race for the White House with 20 days to run.

Not even Republicans disputed that Obama's debate performance was much stronger than the listless showing two weeks earlier that helped spark a rise in the polls for Romney. The two rivals meet one more time, next Monday in Florida.

The first post-debate polls were divided, some saying Romney won, others finding Obama did. At least some of the voters who asked the questions in the town-hall style encounter remained uncommitted. "If Gov. Romney could actually provide the jobs, that would be a good thing because we really need them," said Nina Gonzalez, a 2008 Obama voter, neatly summarizing the uncertainty confronting voters in a slow-growth, high-unemployment economy.

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."

He also jabbed at Romney's remark during Tuesday night's debate that as Massachusetts governor, he received "whole binders full of women" after saying he wanted to appoint more of them to his administration. "We don't have to collect a bunch of binders to find qualified, talented women," he said.

"I've got two daughters and I don't want them paid less for the same job as a man," Obama said at an appearance in Athens, Ohio, later Wednesday.

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.

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Romney's campaign launched a new television commercial that seemed designed to take the edge ever so slightly off his opposition to abortion — another example of his October 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 Chesapeake, Va.

"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.

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.

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).

As the campaign days dwindled down, the number of television commercials rose higher. According to media buyers who track ads, target voters in the area around Cleveland can expect to see an average of about 120 ads next week paid for by the two candidates and groups supporting them — more than 17 a day. There were similar, if somewhat less intense campaign-by-commercials under way across all the battleground states.

In many cases — Florida, Ohio, Wisconsin, Virginia, Nevada among them — competitive races for the Senate and even House contests added to the bombardment. So, too, campaign brochures, piling up in mailboxes earlier than past elections because of widespread pre-election day voting.

There was little mystery in the candidates' concentration on women voters. 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 show gains for Romney among women voters, a shift that Obama can ill afford given the traditional Republican advantage among men.

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.

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."

Vice President Joe Biden's first stop of the day was in Greeley, Colo., where he 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."

Republican Rep. Paul Ryan was in Berea, Ohio, where he said women were suffering under the economy as the end of Obama's term nears. "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."

In a lighter moment, he stopped by the football practice facility of the Cleveland Browns and lamented missing out on hunting season this fall. "I've got this election thing going on," he told Pro Bowl tackle Joe Thomas.

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Associated Press writers Steve Peoples in Chesapeake, Va., Frank Eltman in Mineola, N.Y., Beth Fouhy in New York, Nicholas Riccardi in Greeley, Colo., John Seewer in Berea, Ohio, Ryan Foley in Mount Vernon, Iowa, and Matthew Daly and Kasie Hunt in Washington contributed to this story. Espo reported from Washington.