TAMPA, Fla. -- President Barack Obama and Mitt Romney dueled Thursday across America’s swing states, working feverishly to push early voters to the polls and battling hard for the votes of women.

Obama, his voice hoarse, wrapped up a 48-hour campaign marathon, rolling through Florida, Virginia and Ohio. Romney stumped in Ohio, whose 18 electoral votes could decide the winner in 12 days.

They campaigned as Americans already are voting in 34 states – including key states Colorado, Florida, Nevada and Ohio. Voters in many states can go to the polls or cast “no-excuse” absentee ballots, meaning they don’t have to give a reason for requesting such a ballot, before Election Day. Obama is viewed as having the advantage in early voting states, thanks to the sophisticated get-out-the-vote machine he first used four years ago.

Obama voted himself Thursday in Chicago, the first time an incumbent president has voted early. He implored supporters to do the same. Thirty-five percent of all voters are expected to cast early ballots, up from 31 percent four years ago, according to Paul Gronke, director of the Reed College Early Voting Information Center in Oregon.

Republicans were equally eager to turn out the vote. "I need you to commit as well, not only to vote, and vote early – I won’t say often, just vote early," Romney urged a Cincinnati crowd.

Early voting matters not only because it helps increase turnout, but "it frees up a lot of resources that can be used to get more voters to the polls in Election Day," said Larry Sabato, director of the Center for Politics at the University of Virginia.

The two camps also vied to woo women, as a new AP-Gfk survey confirmed other polls showing that Obama has lost the big lead he had held among women voters. Obama led by 16 percentage points a month ago, but the two are now tied, according to the AP poll.

The president nonetheless saw fresh potential to regain the momentum among women.

"I don’t think any politician in Washington, most of whom are male, should be making health care decisions for women," he told 8,500 people at Tampa’s Ybor Centennial Park. "Women can make those decisions themselves."

His remarks were aimed at women who back the 2010 federal health care law, which Romney wants to repeal and replace, as well as abortion rights supporters.

Democrats also spent Thursday trying to capitalize on comments by Republican U.S. Senate candidate Richard Mourdock of Indiana.

In a debate Tuesday, Mourdock explained his opposition to abortion rights including cases of rape, saying, “I struggled with it myself for a long time, but I came to realize life is a gift from God, and I think even when life begins in that horrible situation of rape, that it is something that God intended to happen.”

Obama, asked about the comment Wednesday by late-night talk show host Jay Leno, said, "Rape is rape. It is a crime. And so these various distinctions about rape don’t make too much sense to me – don’t make any sense to me."

On Wednesday, the campaign unveiled an ad reminding voters that Romney also opposes abortion rights, though Romney’s supports abortion rights in cases of rape, incest or to save the life of the woman.

"Which do you believe?" a woman narrator asks. It then shows several clips of Romney saying the Supreme Court should overturn Roe v. Wade, the 1973 Supreme Court case that established a woman’s right to an abortion. "No matter what Mitt Romney’s ad say, we know what he’ll do," the narrator says.

Romney continued to emphasize his economic message. During an appearance at Jet Machine in Cincinnati, a military equipment supplier and assembler, he outlined his plans after being introduced by women involved in local small businesses. Romney’s advisers maintain he can win the women’s vote with his economic arguments.

"For those of you in your 40s and 50s, who have always anticipated that these would be the high earning years, the most productive years, the years that you’d be able to put a little away for retirement or perhaps help your kids with college,” Romney said, “you’re finding that’s harder and harder to do."

Obama offered his own ideas to a huge crowd at Byrd Park in Richmond, Va.

"I’ve got a plan that will actually create jobs, not just talk about creating jobs; a plan that will actually create middle-class security, not just use the words but not deliver on the promise," Obama said.