(CBS News) After Tuesday night's presidential debate at Hofstra University on Long Island, CBS News' instant poll found that 39 percent of women believed President Obama won, 29 percent believed Gov. Mitt Romney won, and 33 percent called it a tie.

Those numbers represent a highly-prized demographic by both candidates. One of the president's main goals was to bring women back into the fold, and both men shared personal stories designed to appeal to women. In one notable case, however, that may have backfired.

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An audience member, Katherine Fenton, gave both candidates the perfect opening: "In what new way do you intend to rectify the inequalities in the workplace, specifically regarding females make only 72 percent of what their male counterparts earn?"

President Obama was the first to respond, saying: "Well, Katherine, that's a great question, and you know, I was raised by a single mom who had to put herself through school while looking after two kids."

President Obama pointed out that the first bill he signed when he took office gave women more leeway to sue employers over unequal pay.

"I've got two daughters and I want to make sure they have the same opportunities that anybody's sons have," he said.

Romney argued he made hiring women a priority when he was elected governor of Massachusetts in 2002.

"We took a concerted effort to go out and find women who had backgrounds that could be qualified to become members of our cabinet," 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."

But Wednesday, Jesse Mermell, who ran the group that compiled those binders, said this in a conference call with reporters: "To be perfectly clear, Mitt Romney did not request those resumes. After the election, our group approached the Romney transition team with the resumes, or the so-called 'binders full of women.'"

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Obama's debate performance helped among women