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Patricia Zengerle washington
Mr Obama hit hard on issues such as equal pay for women and contraception and abortion rights in the second of three televised presidential debates ahead of the November 6 election.
The topics did not come up in the first debate, when Romney outshone the Democratic president.
Mr Romney has gained ground on the President in opinion polls since the first head-to-head and took the lead in many surveys. Reuters/Ipsos polling data showed the Democrat's support slipping among women, particularly married women.
Fifty-nine percent of married white women backed Mr Romney for president, against only 30.4% who picked Obama, according to data for the week ending October 14. That was a move of around eight points in Romney's favour since before the first debate.
With strong support among women essential to his re-election hopes, Mr Obama devoted much of the second debate toward shoring up their support.
He mentioned the women's health organisation Planned Parenthood five times. He stressed that Mr Romney had promised to stop funding the organisation, which provides contraception and abortions, but also basic services like cancer screenings.
Mr Romney hit back by saying he would help women, and all Americans, by improving the sputtering economy.
However, the Republican offered fewer specifics on women's issues than Mr Obama and at times seemed to stumble.
Jennifer Lawless, director of the Women and Politics Institute at American University, said: "Any ground Mitt Romney gained over the last week or week-and-a-half, he lost tonight."
"Barack Obama was incredibly strong on appealling to women and casting doubt on Mitt Romney's statements."
One of the night's most memorable moments came when Mr Romney was asked how he would ensure pay equity for women. He answered by recalling how, as governor of Massachusetts, he had been concerned when all of the applicants for his cabinet were men.
He said: "I went to a number of women's groups and said, 'Can you help us find folks?' and they brought us whole binders full of women."
Mr Romney's awkward response lit up social media. The user name @RomneyBinders got its own Twitter account, and attracted more than 31,000 followers less than an hour after the debate ended. The hashtag #bindersfullofwomen was one of the 10 most common on the social media service.
Democrats said Mr Romney's answer seemed to show he had few women in his inner circle, and the candidate did not directly address the pay equality issue.
Tara McGuinness, executive director of the left-leaning Centre for American Progress Action Fund, said: "I don't think he substantively engaged on this matter that would make a real difference and that is an important issue in the conversation."
Mr Romney also talked about how he had offered flexible hours so his chief of staff could be with her children when they came home from school.
His comments sounded like "they were from 50 years ago," said Christine Williams, a nurse practitioner from Ohio, who watched the debate in the crucial swing state. In contrast, she said: "When Obama talks about that, it makes my soul sing."
Mr Romney cast his appeal to women in economic terms, repeatedly saying millions of women had lost their jobs in the four years Mr Obama has been President.
He said: "There are 3.5 million more women living in poverty today than when the President took office.
"What we can do to help young women and women of all ages is to have a strong economy, so strong that employers are looking to find good employees and bringing them into their workforce, and adapting to a flexible work schedule that gives women the opportunities they would otherwise not be able to afford."
Mr Obama stressed his support for the Lilly Ledbetter Fair Pay Act, the first bill he signed into law as president, which guarantees equal pay for women workers. His challenger has declined to say whether he supports the law.
Analysts said Mr Obama's performance was likely to stop the loss of support among women voters.
Susan Carroll, senior scholar at the Centre for American Women and Politics at Rutgers University, said: "We'll probably see some movement of women in a more pro-Obama direction. I think some women saw the Obama they hoped to see and were disappointed not to see in the first debate."
Women in a snap poll by the Democratic Lake Research Partners picked Mr Obama as the debate winner by 56% to 34%. Men also gave President the victory, but by a narrower 49% to 43%.
Mr Romney strongly disputed an accusation by Mr Obama that he "feels more comfortable having politicians in Washington decide the healthcare choices that women are making".
He went out of his way to say: "Every woman in America should have access to contraceptives ... the President's statement of my policy is wrong."
Mr Obama scored points by talking about his working mother and grandmother, and his children.
He said: "I've got two daughters and I want to make sure they have the same opportunities that anybody's sons have."
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