WASHINGTON — Two fierce competitors who've given their all, President Barack Obama and Republican Mitt Romney now yield center stage to voters Tuesday for an Election Day choice that will frame the contours of government and the nation for years to come.

After a grinding presidential campaign that packed suspense to the finish, Americans head into polling places in sleepy hollows, bustling cities and superstorm-ravaged beach towns deeply divided. All sides are awaiting, in particular, a verdict from the nine battleground states whose votes will determine which man can piece together the 270 electoral votes needed for victory.

Obama has more options for getting there. So Romney decided to make a late dash to Cleveland and Pittsburgh on Tuesday while running mate Paul Ryan threw in stops in Cleveland and Richmond, Va. Obama opted to make a dozen radio and satellite TV interviews from his hometown of Chicago to keep his closing arguments fresh in voters' minds.

"I feel optimistic but only cautiously optimistic," Obama said on "The Steve Harvey Morning Show." ''Because until people actually show up at the polls and cast their ballot, the rest of this stuff is all just speculation."

Romney, asked on WTAM radio in Cleveland whether he agrees that voters always get it right in the end. "I won't guarantee that they'll get it right, but I think they will," Romney replied.

The GOP nominee then drove to a community center five minutes from his Belmont, Mass., home and cast his ballot with wife Ann at his side. The couple went from the polling site to the airport for his under-the-wire campaign swing.

Vice President Joe Biden and his wife, Jill Biden, were among the first voters Tuesday in at a polling place in Greenville, Del., Biden's home state. Smiling broadly, Biden waited in line with the other voters and greeted them with a handshake. Outside he sent a message to people across the country who may encounter crowded polling places. "I encourage you to stand in line as long as you have to," he told television cameras.

Both sides cast the Election Day choice as one with far-reaching repercussions for a nation still recovering from the biggest economic downturn since the Great Depression and at odds over how big a role government should play in solving the country's problems.

"It's a choice between two different visions for America," Obama declared in Madison, Wis., on Monday asking voters to let him complete work on the economic turnaround that began in his first term. "It's a choice between returning to the top-down policies that crashed our economy, or a future that's built on providing opportunity to everybody and growing a strong middle class."

Romney argued that Obama had his chance and blew it.

"The president thinks more government is the answer," he said in Sanford, Fla. "No, Mr. President, more jobs, that's the answer for America."

With both sides keeping up the onslaught of political ads in battleground states right into Election Day, on one thing, at least, there was broad agreement: "I am ready for it to be over," said nurse Jennifer Walker in Columbus, Ohio.

It wasn't just the presidency at stake Tuesday: Every House seat, a third of the Senate and 11 governorships were on the line, along with state ballot proposals on topics ranging from gay marriage and casino gambling to repealing the death penalty and legalizing marijuana. Democrats were defending their majority in the Senate, and Republicans doing likewise in the House, raising the prospect of continued partisan wrangling in the years ahead no matter who might be president.

If past elections are any guide, a small but significant percentage of voters won't decide which presidential candidate they're voting for until Tuesday. Four percent of voters reported making up their minds on Election Day in 2008, and the figure was 5 percent four years earlier, according to exit polls. In Washington Lee High School in Arlington, Va., hundreds of voters were in line shortly after the polls opened at 6 a.m. and had to wait over an hour to cast their ballot.

By contrast, Election Day came early for more than a third of Americans, who chose to cast ballots days or even weeks in advance.

An estimated 46 million ballots, or 35 percent of the 133 million expected to be cast, were projected to be early ballots, according to Michael McDonald, an early voting expert at George Mason University who tallies voting statistics for the United States Elections Project. None of those ballots were being counted until Tuesday.

The two candidates and their running mates, propelled by adrenalin, throat lozenges and a determination to look back with no regrets, stormed through eight battleground states and logged more than 6,000 flight miles Monday on their final full day of campaigning, a political marathon featuring urgency, humor and celebrity.

Obama's final campaign rally, Monday night in Des Moines, Iowa, was filled with nostalgia. A single tear streamed down Obama's face during his remarks, though it was hard to tell whether it was from emotion or the bitter cold.

Team Obama's closing lineup included Bruce Springsteen, rapper Jay-Z, singers Mariah Carey, Ricky Martin and John Mellencamp, the NBA's Derek Fisher and actors Samuel L. Jackson and Chris Rock. Springsteen, who hitched a ride aboard Air Force One for part of the day, even composed an anthem for the president, rhyming "Obama" with "pajamas."

"Not the best I've ever written," the rocker confessed.

Obama, making his last run for office at the still-young age of 51, was tickled to have Springsteen along as his traveling campaign, telling the crowd in Madison, "I get to fly around with him on the last day that I will ever campaign — so that's not a bad way to end things."

Team Romney's closing events offered a slimmer celebrity quotient, including Kid Rock and country rock performers The Marshall Tucker Band. But the GOP nominee didn't seem to mind.

After a warm welcome at a rally in Fairfax, Va., Romney, 65, told cheering supporters: "I'm looking around to see if we have the Beatles here or something to have brought you. But it looks like you came just for the campaign and I appreciate it."

Wife Ann Romney addressed the crowd in suburban Washington, too.

"Are we going to be neighbors soon?" she asked hopefully.

Ryan alone logged more than 2,500 miles Monday as he hopped from Nevada to Colorado to Iowa to Ohio to Wisconsin.

At a rally in Reno, Nev., he told voters: "This feels like deja vu, doesn't it? You've seen a few of us around, haven't you?" He'd been at a rally just around the corner on Thursday.

Vice President Joe Biden crisscrossed Virginia, and fondly recalled his debate with Ryan during a stop in Richmond.

"You all learned what 'malarkey' means, didn't you?" he said. "Well, I heard a lot of malarkey."

Just in case everyone wasn't paying attention, Obama and Romney made a play for those tuned in to "Monday Night Football," each making satellite appearances on ESPN that aired during halftime of the Philadelphia Eagles-New Orleans Saints game.

The forecast for Election Day promised dry weather for much of the country, with rain expected in two battlegrounds, Florida and Wisconsin. But the closing days of the campaign played out against ongoing recovery efforts after Superstorm Sandy. Election officials in New York and New Jersey were scrambling to marshal generators, move voting locations, shuttle storm victims to polling places and take other steps to ensure everyone who wanted to vote could do so.

Obama, who voted 12 days early, was sure to observe his Election Day ritual of playing pickup basketball with friends and close advisers. The one time he skipped the tradition, he lost the New Hampshire primary in 2008.

"We won't make that mistake again," said senior adviser Robert Gibbs.

Romney was voting at a community center near his home in Belmont, Mass., before his sprint to Ohio and Pennsylvania. His campaign released a gauzy 5-minute Election Day web video called "The Moment" replaying key events from the campaign, with Romney assuring voters, "The future is better than the past."

The election played out with intensity in the small subset of battleground states: Colorado, Iowa, Florida, New Hampshire, Nevada, North Carolina, Ohio, Virginia and Wisconsin. Romney's late move to add Pennsylvania to the mix was an effort to expand his options, and Republicans poured millions into previously empty airwaves there.

In the campaign's final hours, voters around the country echoed the closing arguments of the two presidential candidates.

Obama supporter Gary Muratore, of Upper Arlington, Ohio, said Obama had rescued the country "from the brink of economic disaster."

"And while I don't think the pace of the recovery has been as fast as anyone would like, I think that the only way forward is to keep on the path that he started us down," said Muratore, 62, who attended an Obama rally in Columbus on Monday.

Romney backer Anastasia Loupakos, voting in Iowa City on Monday, said Romney was "the one to turn our economy around."

"I can't stand the thought of Barack as president for four more years," she said. "I couldn't stand him spending all of our money. I feel like he's destroying more jobs than he's creating."

After a long campaign that cost record sums and spawned far more political ads than ever before, Americans were showing fatigue at the end. A Pew Research Center poll released Monday showed 47 percent of Americans followed news about the election closely last week, down from 52 percent a week earlier.

Attorney John Martin, from Golden, Colo., filled out his mail-in ballot over the weekend. He didn't want to reveal whom he had chosen, but said he'd been "obsessively" watching the election for months.

Now, he's ready to move on.

"I'm old enough to be able to live with either outcome," he said.

Sometimes, it all seemed like overkill.

Biden stopped in at Mimi's Cafe in Sterling, Va., after a rally nearby. As one family left, a youngster grumbled, "So we came into the restaurant and still didn't get any food."

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Associated Press writers Nedra Pickler in Washington, Darlene Superville in Arlington, Va., Ann Sanner in Columbus, Ohio, Nicholas Riccardi in Denver, Colo., Ryan J. Foley in Iowa City, Iowa, Philip Elliott in Beloit, Wis., Jim Kuhnhenn and Julie Pace in Chicago, Steve Peoples in Belmont, Mass., and Matthew Daly in Wilmington, Del., contributed to this report.