President Barack Obama and rival Mitt Romney stoked the embers of their smoldering debate as they campaigned through fiercely contested territory less than three weeks before the election.

Hitting the campaign trail on Wednesday -- a day after one of the most contentious presidential face-offs in history -- the two candidates sought the support of women voters and independents who could decide the November 6 vote.

Obama accused Romney of offering a "sketchy deal" by failing to explain how he would pay for across-the-board tax cuts, warning that politicians who wait to get elected before giving specifics often bring unwelcome surprises.

"We're not buying it," Obama told a crowd in Ohio, a key battleground state seen as a must-win for Romney. "We know better, because this is the same sketchy deal that we were sold back in the previous administration."

The 51-year-old Obama, in a tongue-in-cheek aside, implicitly admitted his intense debate showing was a big improvement on a listless performance in the first showdown two weeks ago.

"I'm still trying to figure out how to get the hang of this thing, debating, but we're working on it. We'll keep on improving as time goes on. I've got one left," he said, referring to Monday's foreign policy donnybrook in Florida.

Romney, a multi-millionaire ex-governor of Massachusetts, also said he was pumped up after Wednesday's bare-knuckled debate, in which the two men aggressively paced the stage and repeatedly interrupted each other.

"I love these debates. You know, these things are great. And I think it's interesting the president still doesn't have an agenda for a second term," Romney said in Virginia, another key toss-up state.

Romney blasted Obama as a slick salesman who talked a good game four years ago but has left the country in dire shape.

"The president's policies are running on fumes," he boomed to more than 8,000 people at a rally in Leesburg, where one man held up a "Democrats 4 Romney" sign.

Obama mocked Romney for telling the 65 million people watching the debate on television that he had combed through "binders full of women" while recruiting females for his cabinet when he was governor of Massachusetts.

Obama used the oddball phrase to criticize Romney over women's health care and equal pay, while highlighting his own record on women's rights and the need to hire more math and science teachers.

"We don't have to collect a bunch of binders to find qualified, talented, driven young women, ready to learn and teach in these fields right now," Obama told a crowd in a muggy gym at a liberal arts college in Iowa.

Romney also reached out to women, who could make a difference in key swing states like Iowa, Ohio, Virginia and Florida.

"This president has failed America's women," he told supporters.

A fresh Gallup daily tracking poll showed Romney up six points among likely voters in his best showing yet, suggesting Obama's strong rebound after the first debate came just in the nick of time for his supporters.

A new survey by Marquette University, of traditionally Democratic Wisconsin, showed Obama up by a single point.

Neither poll included data reflecting the impact of Tuesday's debate, but with the respected RealClearPolitics average of polls showing just a 0.4 percent lead for Romney, strategists from both campaigns acknowledged that the November 6 election could be agonizingly close.

"I am not too proud to beg. I want you to vote," Obama said in Athens.

In an apparent effort to beef up rallies, the Obama campaign said rock star Bruce Springsteen would campaign for the president Thursday, appearing with former president Bill Clinton in Parma, Ohio and at an event in Ames, Iowa.

"President Obama is our best choice because he has a vision of the United States as a place where we are all in this together," Springsteen said in a statement distributed by the campaign.

The political class was still digesting the repercussions of the second debate, which included questions from undecided voters.

Ad hoc polls from major broadcasters gave Obama the edge, while analysts agreed that the Romney surge had hit a speed bump, leaving a close race.

As Obama spent a few hours in Iowa on Wednesday, 13 people took out a full-page ad in the Des Moines Register announcing their apology for voting for him four years ago and their intent to pull the lever for Romney in November.

Obama "has offered disappointment after disappointment," they wrote. "It turns out that eloquence does not equal competence. We'll gladly admit: we were wrong."

The 13 people were named in the ad, which was paid for by the Romney campaign.