FAIRFAX, Virginia (AFP) — Barack Obama and Mitt Romney both confidently predicted victory yesterday as they rallied supporters in the dying hours of a bitter White House race, which the US president leads by a whisker.

The foes, drained by fatigue, charged through the swing states that will dictate their fates, taking final shots at one another hours before polls open in an election that will decide whether Obama wins a second White House term.

“This is a campaign about America and about the future that we will leave to our children and their children,” Romney told raucous supporters in the battleground state of Virginia.

“We thank you and ask you to stay with it all the way until we win tomorrow night,” Romney said, sparking wild cheers.

Obama, with rock legend Bruce Springsteen and rapper Jay-Z, delivered a similar message in the liberal college town of Madison, Wisconsin, pleading with supporters to stick with him in a final push to the finish.

“If you’re willing to work with me again, and knock on some doors with me, make some phone calls for me, turn out for me, we’ll win Wisconsin. We’ll win this election. We’ll finish what we started,” he said.

Election eve polls cemented the impression that Obama has the slightest of leads after a campaign that has cost billions of dollars, but cannot take victory, and the historical validation of re-election for granted.

The final national polls showed an effective tie, with either Romney or Obama favoured by a single point in most surveys, reflecting the polarised politics of a deeply divided nation.

Obama was, however, up by three points in national polls conducted by Pew Research and by the Washington Post and ABC News, suggesting that if either candidate could boast of 11th-hour momentum, it was the 44th US president.

His last line of defence in the industrial midwest also seemed to be holding: Obama led the RealClearPolitics.com average of polls in crucial Ohio by three per cent, and was up by 2.4 points and 4.2 points in Iowa and Wisconsin.

Should those polls be reflected in vote totals today, Obama would become only the second Democrat, after Bill Clinton, to win a second four-year term since World War II.

Obama was also up by a narrow margin in swing states Virginia, New Hampshire, Colorado and Nevada while Romney led by similarly thin margins in poll averages of Florida and North Carolina.

Romney’s camp, however, insists that the former Massachusetts governor will profit from an anti-Obama wave on Tuesday and contends the polls overstate the proportion of Democrats in the electorate and Republican enthusiasm.

Obama’s team, however, cheered by early vote data and the neighbourhood-by-neighborhood political machine the president has assembled, insisted that they would be vindicated by the election.

“We’re going to win the electoral vote and we’re going to win the popular vote,” said Obama’s political guru David Axelrod.

“It’s going to be a close election as we always said. This is the season for weird theories, but we’re very, very confident of both those things.”

Romney fired the first shots yesterday, as a crowd shouted, “One More Day, One More Day!” before heading onto Virginia, Ohio, and with plans to finish up for the night in New Hampshire.

But his campaign did not end last night, as Romney announced plans to visit local campaign offices and help get out the vote in Ohio and Pennsylvania today.

Obama, increasingly wistful, in what will be his last day on the campaign trail, win or lose, dismissed Romney’s latest claim to being an agent of change, taking the stage after Springsteen rocked an 18,000 strong crowd in Madison.

“You have seen the scars on me to prove it. You’ve seen the gray hair on my head to show you what it means for fight for change, and you have been there with me,” he said.

Springsteen told the crowd that his life in music had been dedicated to charting the distance between the American dream and American reality.

“Our vote tomorrow is the one undeniable way we get to determine the distance in that equation,” said The Boss, who was traveling with Obama aboard Air Force One.

Obama planned to return home to Chicago last night to await the outcome of the election, in which he seeks to defy conventional wisdom that high unemployment and a sluggish economy doom incumbent presidents.

His campaign deployed former President Bill Clinton to Pennsylvania, ostensibly a safe Democratic state, but one which has seen a late run by Romney — evidence, according to Obama’s team, of desperation.

“I’m for President Obama because … he’s got a much better plan for the future,” said Clinton, who has overcome acrimony left over from Obama’s 2008 primary defeat of Hillary Clinton, to embrace the president.

Florida, famous for the presidential election debacle 12 years ago which required the hand-counting of thousands of ballots, faced some new election-related problems ahead of today’s vote.

The state’s Democratic Party filed a federal lawsuit Sunday over long delays encountered by some voters who were unable to cast votes in southern Florida despite spending hours in line.