The longest and most expensive presidential race in history drew at last to a frantic, frenzied close last night, with Barack Obama and John McCain hopscotching across America, panning for the final errant votes in key battleground states and trading eleventh-hour attacks on the economy, jobs and environmental policy.

In the final hours of the campaign, Mr Obama meanwhile found himself distracted by personal bereavement, announcing that his 86-year-old grandmother, Madelyn Dunham, had died after a battle with cancer. He said that he learnt of her death yesterday morning while he was still campaigning in Jacksonville, Florida. "She was the cornerstone of our family, and a woman of extraordinary accomplishment, strength, and humility," he said in a joint statement with his half sister, Maya Setoro-Ng. "She was the person who encouraged us and allowed us to take chances."

Mr McCain issued condolences to his opponent on hearing the news. "Our thoughts and prayers go out to them as they remember and celebrate the life of someone who had such a profound impact in their lives," the statement by John and Cindy McCain said.

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Last month, Obama took a break from campaigning and flew to Hawaii to be with Dunham as her health declined but yesterday he planned to complete his campaign commitments.

At least one million people are expected to converge on Grant Park in downtown Chicago tonight, hoping to witness Mr Obama taking the stage in the day's dwindling hours to declare victory and to celebrate becoming the first African American to capture the land's highest office.

With the soaring skyline of the Chicago Loop and the pale waters of Lake Michigan as the backdrop, the event site featured a large catwalk-style stage for Mr Obama to make his address. For the first time, it featured two tall bulletproof glass barriers on either side of the podium, amid heightened concerns for his safety.

While the polls continued to give the fuller wind to the Democrat, his Republican opponent stayed scrapping to the end, embarking on a gruelling 17-hour swing through Pennsylvania, Indiana, New Mexico, Colorado and Nevada. Mr McCain will wind up his campaign with a rally in Prescott, Arizona, this morning before presiding over his own election night party in a Phoenix hotel.

"There is one day left until we take America in a new direction my friends," Mr McCain said, his only hope for victory resting on capturing nearly all the remaining undecided voters and additionally peeling away some of Mr Obama's supporters.

He is also counting on the base of his own party coming out and defying the enthusiasm gap between Republicans and Democrats. That so few turned up to see him yesterday was an ill omen – George Bush drew a crowd of 14,000 for an eve-of-election event in the same Tampa venue four years ago, Mr McCain barely managed 1,000.

Mr Obama, whose blitz of media interviews yesterday took him even into the territory of young men and visible underwear – he told MTV he wished young men would keep the waistbands of their jeans somewhere close to their waists – kicked his day off in Jacksonville, Florida, in an arena where, weeks before, Mr McCain asserted that the fundamentals of the US economy remained "sound".

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Mr Obama mocked the now infamous economic analysis of his rival. "Florida, you and I know that's not only fundamentally wrong, it also sums up the fact that he is so out of touch," the Illinois senator declared, triggering a ripple of jeering from the crowd. "You don't need to boo," he replied without pause. "You just need to vote."

Officials in many states are bracing for polling stations to be swamped and legal challenges to be launched if the results are close. A record turnout is expected after a 21-month marathon that has gripped America like no election in generations. As many as one-third of all ballots had been cast even before today as more states than ever allowed early voting. Offering possible encouragement to the Obama camp, officials in most of those states reported that a heavy majority of those who got in line early described themselves as Democrats.

Little separated most eve-of-voting polls. Among the last polls, Fox News gave Mr Obama 50 per cent nationally to 43 per cent for Mr McCain. An NBC/Wall Street Journal poll gave Mr Obama a 51-to-43 lead.

How long it will be before the country and the world knows which way voters have gone will depend on whether Mr Obama achieves the blowout some expect or if tonight turns out to be a nail-biter. The first clues will come at the closing of the polls in Indiana (at 11pm GMT) and Virginia one hour later. Both states historically vote Republican but are thought to be in play tonight. Also under the microscope will be Pennsylvania, a state with 21 electoral college votes that Mr McCain really has to win if he is to have any hope of stopping the Obama tide but where polls have persistently shown him behind.

The passion felt by the supporters of each candidate may be more intense than anybody can remember; thus terrible disappointment is now just hours away for one set of supporters.

Officials in Chicago, Mr Obama's home town where he will watch the returns tonight, know that Grant Park – the lakeside patch of grass that was the site of clashes between police and anti-Vietnam War protesters in 1968 – might be the scene of one of the biggest victory parties the world has ever witnessed – or the world's biggest, most disconsolate political wake.