CHESAPEAKE, Va -- . President Barack Obama and Mitt Romney, energized by their showings at a debate whose impact was still being debated, revved up eager swing state audiences on Wednesday with pointed partisan appeals.

Their Tuesday night battle in Hempstead, N.Y., reverberated throughout the political world Wednesday, and each candidate’s approach to women’s issues appeared to be responsible for some of the louder echoes.

Obama’s forces pounded their Republican challenger on his assertion during the debate that he had “binders full of women” to choose from for state jobs from while governor of Massachusetts.

In Mount Vernon, Iowa, Obama was introduced by a college junior who is majoring in English and women’s studies. The president spoke enthusiastically in a steamy gym, a pink breast cancer bracelet flashing on his right wrist.

He referred to Romney’s “binder” remark and earned a roar as he talked about boosting spending on education. He said that “we don’t need a bunch of ‘binders’ to find qualified, talented women willing to teach.”

During the debate, Romney said that when he was governor, “we took a concerted effort to go out and find women who had backgrounds that could be qualified to become members of our Cabinet. 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."

The remark triggered an immediate explosion in social media, with blogs, Twitter postings and websites all trying to making comic or political hay out of Romney’s choice of words.

In Virginia, one of a handful of pivotal states, Romney didn’t mention the “binders” comment but hammered at Obama for promoting a badly flawed plan for fixing the ailing economy. Speaking to a cheering crowd of about 3,500 at an outdoor rally outside Tidewater Community College, the Republican nominee countered that Obama has no coherent plan for helping women survive the struggling economy.

“This president has failed America’s women,” Romney said, citing economic data showing more women without jobs and in poverty than when Obama took office.

Obama, who offered a scrappier version of himself at the Tuesday night debate than he did at his first faceoff with Romney, joked in Iowa that he was still “getting a hang on this thing. We’re working on it, we’ll keep on improving.”

The president’s aggressive approach, in sharp contract to his first encounter with Romney, seemed to quell anxieties among his supporters. He spent most of his time hammering his opponent on nearly every issue that came up Tuesday night.

Obama ridiculed Romney for not providing details on what tax breaks he’d target to pay for his 20 percent cut in income tax rates, and joked that Romney’s only offerings have been “getting rid of Big Bird and ending wind energy tax credits.”

Congress’ Joint Committee on Taxation staff has said that even eliminating most popular deductions would support only a 4 percent rate cut.

“You’ve heard of the New Deal, the Fair Deal and the Square Deal,” Obama said. “Mitt Romney is trying to sell you a sketchy deal. You know better. We’ve been there.”