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Republican John McCain hopscotched across America yesterday, staging seven last-ditch rallies across seven must-win battleground states in a final, perhaps futile, comeback attempt to win the presidency.

Barack Obama, his Democrat rival, was comfortably ahead in the polls, after the longest and costliest presidential campaign in history. He spent a far less frenetic day than his septuagenarian opponent, with events in several states before he returned to spend the night in the Windy City, where he launched his political career.

A huge election night victory rally, with as many as a million people expected, is planned for Chicago's waterfront, and workmen are frantically readying the Grant Park site.

Late yesterday afternoon, it became known that Mr. Obama, 47, had spent the last day of the long, gruelling pursuit of the presidency travelling with the poignant knowledge that his grandmother, a white woman who had played a key role in his upbringing from the age of 10, had died overnight in Hawaii, just as he seemed on the cusp of making history.

Last month, Mr. Obama left the campaign trail for a last visit with his deceased mother's mother, Madelyn Dunham, 86 and gravely ill with cancer.

"She was the cornerstone of our family, and a woman of extraordinary accomplishment, strength and humility," Mr. Obama and Maya Soetoro-Ng, his half-sister, said in a joint statement yesterday. The family said a private ceremony would be held later.

Mr. McCain sent his condolences to Mr. Obama but the two were soon exchanging nasty, long-distance barbs in the last hours of the campaign.

Both claimed to be on the verge of becoming the 44th president.

"We are one day away from change in America," said Mr. Obama, who if victorious, would be the first African-American to reach the Oval Office. At a rally in North Carolina, he became choked up as he paid tribute to his grandmother, calling her one of the "quiet heroes" that "sacrifice for their children and their grandchildren. In just one more day we have the opportunity to honour all those heroes," he said.

With an extraordinary final push that covered more than 3,000 kilometres, Mr. McCain, his voice raspy and worn, told supporters in seven states that the polls were wrong and he was about to pull off a historic upset. Pollsters and pundits alike have all but written him off, but the former naval aviator who spent five years as a prisoner of war, has twice before resurrected a political career that seemed finished.

"We will win; ... don't give up hope, be strong," Mr. McCain said. And he derided his rival for overconfidence: "My opponent is measuring the drapes in the White House."

He also tried to paint Mr. Obama as a dangerous left-winger. "He's more liberal than a guy who calls himself a socialist and that's not easy."

Mr. McCain's campaign got one bit of good news yesterday. The Alaska Personnel Board cleared running mate Sarah Palin of wrongdoing in an abuse-of-power investigation into the firing of the state's public safety commissioner. The three-member panel under Ms. Palin's authority contradicted a legislative inquiry that concluded she had abused the power of her office by pressuring subordinates to fire a state trooper involved in a feud with her family.

Mr. Obama urged his backers not to rest easy or be lulled by polls showing him poised for a sweeping victory and, instead, battle hard until polls close.

After an early-morning Florida rally, Mr. McCain flew to Pennsylvania, Tennessee, Indiana, New Mexico, Colorado and Nevada before ending a 17-hour day early this morning with a rally in Prescott, Ariz., where he has always concluded his Senate campaigns.

The Republican's itinerary revealed the scope of the task facing him. All but one of those states, Pennsylvania, voted for Mr. Bush four years ago. And Mr. McCain is fighting a rearguard action in six of them.

Mr. Obama spent his last campaign day, and launched another flurry of TV advertising, on traditional Republican turf, seeking to turn more supposedly safe red states into the purple swing states and perhaps even add them to the Democrat blue tide. He made campaign stops in Florida, North Carolina and Virginia, all states won by Mr. Bush in 2004 and now seemingly on the verge of going Democratic.