Mitt Romney could face huge hurdle with women voters in swing states

(CBS News) WASHINGTON - A Quinnipiac University/CBS News/New York Times poll released Wednesday in three key swing states shows President Obama leading his Republican rival, especially among female voters.

Traditionally, Democrats do better among women than Republicans, but the gender gap in this poll was remarkable: more than 20 points in Ohio and Pennsylvania.

Pollsters say it's the president's message that's pulling women in.

Campaigning in Ohio Wednesday, Mr. Obama pushed the notion that government isn't the only solution, but it should play a role in boosting the economy -- especially for the middle class.

Pollsters say that message resonates, particularly with single women struggling to get by.

Those women chose the president over the presumptive Republican nominee, Mitt Romney, by 2-to-1 in the poll.

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Women are also more likely to list health care and social issues as important to their vote, which is why you're likely to see more ads like one that's out from the Obama campaign featuring a woman who says, "It's a scary time to be a woman. Mitt Romney is just so out of touch."

Women make up a key constituency. In 2008, 53 percent of voters were women.

Peter Brown, of the Quinnipiac Polling Institute, helped conduct the poll.

He says that to close the gap, Romney must convince women he understands their concerns. "He needs to increase his margin among married women and reduce the president's margin among single women," says Brown.

Romney does lead among men in the same two states: in Ohio by 10 points and in Pennsylvania by three. The president won among male voters in 2008 by 1 percentage point.

"We've seen this gender gap before. So this isn't unusual," Obama campaign senior strategist David Axelrod told CBS News. "I think there are some issues to which women are particularly attuned."

But the Obama campaign did not have a ready answer for why the president trails Romney among men.

To see the Nancy Cordes report, click on the video in the player above.

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    Nancy Cordes is CBS News' chief White House correspondent.