It could become a metaphor for a long night ahead: the first 10 votes cast today in the US election race were split evenly between Barack Obama and Mitt Romney.

Polling booths opened in the village of Dixville Notch in New Hampshire on the stroke of midnight local time. After 43 seconds of voting they were quickly counted, resulting in a tie with five votes each for Obama and Romney.

The two contenders spent the eve of election jetting across key swing states as pollsters suggested the outcome later tonight will be very close, although the president has a slight edge.

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Obama appeared in Iowa, Wisconsin and Ohio, joined at rallies by Bruce Springsteen and rapper Jay-Z, and ended his campaign in Des Moines, Iowa, where his run for the presidency began in 2007. At a late-night rally, he told the crowd that Iowa had started "a movement that spread across the country".

Romney, who would become the first Mormon US president if he wins, yesterday went to Florida, Virginia, Ohio, and New Hampshire, before surprising observers by announcing that he plans to extend campaigning into election day by visiting Ohio and Pennsylvania later today, before returning to his Boston home to wait for the returns.

A spokeswoman said Obama will not campaign today, but remain in his home town of Chicago and reach out to swing-state voters through a series of television and radio interviews.

Near to Dixville Notch, in the village of Hart's Location, the second votes cast showed Obama had "won" with 23 votes, while Romney received nine and Libertarian Gary Johnson polled one. The 33 votes were cast in five minutes, 42 seconds.

The two locations have been enjoying their first-vote status since 1948 and it is a matter of pride to get everyone to the polls.

Hart's Location selectman Mark Dindorf said you could call it a friendly competition to see whose votes were tallied first - but added that Hart's Location was a town and Dixville Notch a precinct.

Obama and Romney are running almost neck-and-neck in national polls, in a campaign that has cost more than £1.2bn. But surveys of the battleground states that will determine the election show Obama narrowly ahead.

The race has been most intense in Ohio - no Republican has ever made it to the White House without winning there.

In Fairfax, Virginia just outside Washington DC, Romney, a former Massachusetts governor said the president had failed to deliver on the promise of his 2008 campaign and it was time for a new direction.

"Look at the record. Talk is cheap, but a record is real and it's earned with effort. When the president promised change, you can look and see what happened. Four years ago then-candidate Obama promised to do so very much but he's done so very little."

In Ohio, Bruce Springsteen and rapper Jay-Z helped warm up a crowd for Mr Obama before the president appeared.

"I've got a lot of fight left in me and I hope you do," Mr Obama told the rally, his voice hoarse from nearly non-stop campaigning.

"The folks at the very top in Washington don't need another champion. They'll always have a seat at the table. The people who need a champion are the people whose letters I read every day. We've come too far to turn back now. We've come too far to let our hearts grow faint."

Thirty million Americans have already cast their ballot through early voting across 34 states. In the 2008 presidential election, 130 million people voted.

With the election expected to be decided by a razor-thin margin, both sides are readying teams of lawyers for legal fights.

Efforts are being made to help people in New York and New Jersey still facing multiple problems after Superstorm Sandy get to the polls.

State officials have said that in counties declared emergency zones voters can fill out an affidavit ballot at any polling place they can reach.

Sandy killed more 100 people in 10 states but hit New Jersey and New York hardest. A week after the storm hit the mid-Atlantic and the North East, more than a million homes and businesses remain without power.