Candidates Court Women Voters; Post-Debate Polls Divided on Winner, but Even Republicans Acknowledge Obama Improved Performance; ELECTIONS 2012: Presidential Debate Aftermath - POLITICS

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MOUNT VERNON, IOWA - 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, on 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.

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. …