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The 47-year-old Democrat was "the most significant breakthrough candidate in all American history", he said.
"He could do for race in America what John F Kennedy did for religion in America.
"Kennedy governed as a president of all America, proving that a (Roman) Catholic would not be a Catholic president, but a true American president.
"And ever since then the issue of Catholicism has been non-existent."
He went on: "If Obama wins and Obama governs as the president of all Americans, as I'm confident he will, he can do to the issue of race the same kind of transformations that John F Kennedy achieved for the issue of Catholicism in 1960."
An "entire political era" will change as the results come in tonight, he said. "2008 will mark the end of the conservative era and a beginning of a new political era in the United States.
"It will surely come to an end if, as expected, Barack Obama wins the election. He will bring with him a strong Democratic Congress... and he will have a chance to put his stamp on national policy and national life, just as Ronald Reagan did when he came in 1980 and began the conservative era.
"Even if there should be an upset and John McCain wins, it will not mark the continuation of the conservative era.
"John McCain will also have a strongly Democratic House and a strongly Democratic Senate. He will not be able to turn back the clock to the policies of George W Bush. He has pledged to be fundamentally different."
On Monday, as the candidates swept through a series of key battleground states in a last-minute bid for the support of any undecided voters who could tip the election in their favour, Mr Obama received news that his 86-year-old grandmother Madelyn Dunham had died of cancer.
He described her as the "cornerstone of our family" but vowed to fight on to "change the country and change the world".
Speaking at a rally in Charlotte, North Carolina, just two hours after the announcement, he said: "She was one of those quiet heroes that we have all across America." Speaking in a sombre tone to a silent audience, he went on: "They aren't seeking the limelight; all they're trying to do is to do the right thing.
"That's what America's about, that's what we're fighting for.
"We have the opportunity to honour all those quiet heroes all across America and all across North Carolina.
"We can bring change to America to make sure that their work and their sacrifice is honoured. That's what we're fighting for."
Earlier, Mr McCain declared "the Mac is back" as he set off to get out the vote by making seven stops in the final day.
The 72-year-old Arizona senator, whose running mate Sarah Palin would be the first female US vice president if the Republicans win, told cheering supporters in Tampa, Florida: "With this kind of enthusiasm and this kind of intensity, we will win Florida and we will win this race.
"We need to bring real change to Washington and we have to fight for it."
The latest polls showed 228 of the 270 electoral votes needed to win the presidency were considered to be in safe Democratic hands, according to RealClearPolitics.com. A further 50 electoral votes are thought to be leaning towards Mr Obama.
For the Republicans, 118 electoral votes are considered safe with another 14 leaning towards Mr McCain, leaving 128 electoral votes from so-called "toss-up" states. Florida and Ohio are two of the closest-fought states in the nation and together they offer 47 electoral votes to the winner.
North Carolina, Virginia, Indiana, Nevada and Colorado will also be key to watch as the results come in - all were won by Mr Bush on the Republican ticket in 2004, but have been made competitive by Mr Obama's record-shattering fundraising operation which saw his campaign bring in 150 million dollars (£95.2m) in September alone. Pennsylvania will also be key as Mr McCain has made an aggressive for the usually-Democratic state and the race there has narrowed from 14 points three weeks ago to 7.6 points.
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