WASHINGTON: Americans headed to the polls Tuesday after a burst of last-minute campaigning by President Barack Obama and Mitt Romney in a nail-biting contest unlikely to heal a deeply polarized nation.

The time for obsessing over the latest swing state opinion polls was over as the greatest political show entered its thrilling finale after an 18-month roller-coaster ride that has gone right down to the wire.

The most expensive campaign in history, and one of the most negative, saw more than $6 billion unleashed by the rival camps in a fight to persuade the American people over very different visions of the future.

Voters will decide whether to re-elect Obama despite the plodding economy or hand the reins to Romney, who has vowed a return to prosperity through smaller government.

Democrat Obama, 51, leads his Republican foe by a whisker heading into polling day as he seeks to defy historical precedent that suggests incumbent presidents fail to win a second four-year term at times of high unemployment.

Romney, 65, a former Massachusetts governor blasted by critics as a rich plutocrat indifferent to middle class pain, would make history as the first Mormon president and promises to ignite economic growth and job creation.

Polls opened in the first clutch of eastern states -- including battlegrounds New Hampshire and Virginia -- from 6:00 am (1100 GMT), with the rest of the country's six mainland time zones following suit through the day.

Within 20 minutes of polls opening dozens of voters were lined up outside stations in northern Virginia, an early sign of enthusiasm in a state where the two candidates are locked in a virtual tie.

In a quaint slice of Americana, the 10 voters in the hamlet of Dixville Notch, in northern New Hampshire, played their traditional roll of casting the first votes in the election as the clock struck midnight.

And in a possible precursor of a dramatic night ahead, Obama and Romney were tied at five votes each, a historic first.

Both men, exhausted by the last manic Monday of a campaign that has raged for two years, made their final, heartfelt plea to voters in late night rallies attended by fervent supporters.

"Tomorrow, from the granite of New Hampshire to the Rockies of Colorado, from the coastlines of Florida, to Virginia's rolling hills, from the valleys of Ohio to these Iowa fields, we will keep America moving forward," Obama said.

Speaking in Iowa, the state that first nurtured his White House dreams in 2008, a single tear rolled down the president's face as he wrapped up what was -- win or lose -- his last-ever campaign event.

Romney put an exclamation mark on his campaign with his own, rowdy late night rally, at a sports arena in New Hampshire.

"Tomorrow is a moment to look into the future and imagine what we can do, to put that past four years behind us and build a new future," Romney said.

Voters are not solely picking a president for the next four years.

They will also cast judgement on a third of the Democratic-led Senate and the entire Republican-run House of Representatives. But with neither chamber expected to change hands, the current political gridlock will likely linger.

A dispiriting White House race, so different from Obama's euphoric change crusade of 2008, produced the election both sides expected -- a frantic scrap for thin victory margins in 10 or so swing states.

Obama, the first African American president, on Tuesday led by the slimmest of margins in averages of national polls, which measure the likely popular vote, possibly helped by his leadership during superstorm Sandy.

The president's early voting and polling leads in battleground states also stirred confidence in his campaign team.

Romney aides, however, predicted a surge of enthusiasm for the Republican would confound state polls, which they said overestimated the likely Democratic turnout and did not register the undercurrent of antipathy for Obama.

The central message of Obama's campaign has been that he saved America from a second Great Depression after the economy was on the brink of collapse when he took over from president George W. Bush in 2009.

He claims credit for ending the war in Iraq, saving the US auto industry, killing Osama bin Laden, offering almost every American health insurance, and passing the most sweeping Wall Street reform in decades.

Striking a populist theme, Obama said he would not rest until every American got a "fair shot" in an economy not rigged by the rich, and sought to disqualify Romney as a potential president with a barrage of negative ads.

Romney sought to mine frustration with the slow pace of the economic recovery and argued that the president was out of ideas and had no clue how to create jobs, with unemployment at 7.9 percent and millions out of work.

No president since World War II has been elected with the unemployment rate above 7.4 percent, and Obama is hoping to avoid the fate of a host of European leaders who paid for the economic crisis with their jobs.

US elections are not directly decided by the popular vote, but require candidates to pile up a majority -- 270 -- of 538 electoral votes from the 50 states and Washington, DC, calculated indirectly on the basis of population.

A candidate can therefore win the nationwide popular vote and still be deprived of the presidency by falling short in the Electoral College.

Obama seems to be clinging on to a last line of defense in the Midwestern states of Ohio, Wisconsin and Iowa, which would, in conjunction with safe Democratic states, guarantee him re-election.

In poll averages calculated by the RealClearPolitics website, Obama led in Iowa (by 2.4 percent), Ohio (2.9 percent), Wisconsin (4.2 percent), Virginia (0.3 percent), New Hampshire (2.0 percent), and Colorado (1.5 percent).

Romney led by 1.5 percent in the biggest swing state, Florida, and in North Carolina, which Obama won by just three percent, or 14,000 votes, in 2008.

American voters will also weigh in on more than 170 state-wide ballots for everything from gay marriage to marijuana and abortion to electoral maps.

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