President Barack Obama and Republican challenger Mitt Romney closed out their hard-fought and deeply negative battle for the White House, leaving Americans voting Tuesday with a stark choice between fundamentally opposing visions for the country.

After months of campaigning and billions of dollars spent in the battle for leadership of the world's most powerful country, Obama and Romney were in a virtual nationwide tie, an overt symptom of the vast partisan divide separating Americans in the early years of the 21st century.

Obama appeared to have a slight edge, however, in the decisive swing states that saw a frenzy of last-minute attention from both candidates on Monday. Those states — nine in this election year that are not seen as reliably in either the Republican or Democratic camp — will be critical in deciding which man wins the required 270 electoral votes.

Under the U.S. system, the winner of the presidential election is not determined by the nationwide popular vote but in state-by-state contests. The candidate who wins a state — with Maine and Nebraska the exceptions — is awarded all of that state's electoral votes, which are apportioned based on representation in Congress.

After stops earlier in Wisconsin and Ohio, Obama closed out his campaign in Des Moines, Iowa, late Monday, returning to the state which put him on the road to the Democratic presidential nomination with a 2008 victory in the lead-off caucuses over Hillary Rodham Clinton, now his secretary of state. He planned to spend Election Day at his home in Chicago, where he will hold his post-election rally — win or lose.

In an event steeped in nostalgia, the president urged voters in Iowa to help him finish what they started here four years ago.

"I've come back to Iowa one more time to ask for your vote," Obama told 20,000 supporters at the outdoor rally. "This is where our movement for change began."

After rallies in Florida, Virginia and Ohio, Romney returned Monday night to New Hampshire, where he won the state's first-in-the-nation primary in January, speaking to about 10,000 people at the Verizon Wireless arena.

Romney assailed Obama's economic policies amid the recession, and promised to bring change that he asserted Obama had only talked about.

"Talk is cheap, but a record is real," Romney said.

With many of the late polls in key states tilting slightly against him, Romney decided to campaign on Election Day in Ohio and Pennsylvania, before returning to his Boston home to wait out the returns.

Romney has made a late-campaign drive for Pennsylvania, a state that had been seen as solidly in the Obama column. The move was widely seen as a push — perhaps against all odds — to compensate for Obama's expected victory in Ohio.

The presidency aside, there are 33 Senate seats on the ballot Tuesday, and according to one Republican official, a growing sense of resignation among his party's rank and file that Democrats will hold their majority in the 100-member Senate.

The situation was reversed in the House of Representatives, where Democrats made no claims they were on the verge of victory in pursuit of the 25 seats they need to gain control. All 435 House seats are at stake.

The likelihood of another divided Congress means that whoever wins the White House will have to contend with the same partisan legislative struggles that dogged Obama's term.

Fitting for a tight election, voters in tiny Dixville Notch, New Hampshire, split over the candidates, Obama and Romney receiving five votes each when balloting took place at midnight. In nearby Hart's Location, the hamlet that shares the traditional honor of casting the first presidential ballots on Election Day, Obama won with 23 votes, Romney received nine and Libertarian Gary Johnson received one.

More than 30 million absentee or early ballots have already been cast, including in excess of 3 million in Florida.

Obama and Romney, a former Massachusetts governor and the ultra-wealthy founder of a private equity firm, have spent months highlighting their sharp divisions over the role of government in Americans' lives, in bringing down the stubbornly high unemployment rate, reducing the $1 trillion-plus government spending deficit and reducing a national debt that has crept above $16 trillion.

The economy has proven a huge drag on Obama's candidacy as he fought to turn it around after the near financial meltdown shortly before he took office and the deepest recession since the Great Depression of the 1930s, a downturn that was well under way when he replaced George W. Bush in the White House on Jan. 20, 2009.

The candidates' opposing views on other issues from gay marriage to abortion rights have only added to the divisive atmosphere.

"This is not just a choice between two candidates or two parties. It is a choice between two visions," Obama told nearly 20,000 people in Wisconsin.

"Our choice tomorrow is going to lead to very different outcomes," Romney said at a rally in Virginia. If elected, Romney would be the first Mormon U.S. president.

Obama insists there is no way reduce the staggering debt and safeguard crucial social programs without asking the wealthy to pay their "fair share" in taxes. He hammered on Romney's shifting positions and said the Republican's proposals amount to the same "top-down policies that crashed our economy" in the first place.

"It's not about just about policies. It's also about trust," Obama said. "You know where I stand. You know what I believe. You know I tell the truth."

In surveys of the battleground states, it appeared Obama held small advantages in Nevada, Ohio, Iowa and Wisconsin — enough to deliver a second term if they held up, but not so significant that they could withstand an Election Day surge by Romney supporters. Romney appears to be performing slightly better than Obama or has pulled even in North Carolina, Virginia and Florida.

The biggest focus has been on Ohio, an industrial state that has gone with the winner of the last 12 presidential elections. Ohio was the only state both candidates visited Monday. No Republican has ever won the White House without carrying Ohio.

Vice President Joe Biden and Republican running mate Paul Ryan of Wisconsin also went through their final campaign paces on Monday in the handful of battleground states. Both campaigns say the winner will be determined by which campaign is better at getting its supporters to the polls.

The president needs the overwhelming support of blacks and Hispanics to counter Romney's big lead among white men. At the same time, his support among minorities may have cooled slightly since the 2008 vote when there was the euphoria of making history by electing America's first black president.

Romney, who described himself as "severely conservative" during the Republican primary campaign, has shifted sharply in recent weeks to appeal to the political center, highlighting his claim to have been deeply bipartisan when he was governor of Democratic-leaning Massachusetts.

Still, he did not shy away from highlighting his differences with Obama, saying the president's proposal to raise taxes on the highest earners would discourage hiring just when the country needs it most. Romney, who claims his successful business background gives him the expertise to manage the economy, favors lowering taxes and easing regulations on businesses.

"The president thinks more government is the answer. More jobs is the answer, America," Romney said in Virginia.

The final Washington Post-ABC News tracking poll, released Monday, showed Obama with support from 50 percent of likely voters to 47 percent for Romney. The poll had a margin of error of 2.5 percentage points.

The final national poll from the Pew Research Center found Obama with a three-point edge over Romney, 48 percent to 45 percent among likely voters, an improved showing that indicates the president may have benefited from his handling of the response to last week's Superstorm Sandy. Obama suspended three full days of campaigning to deal with the East Coast disaster. The poll had a margin of error of 2.2 percentage points.