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A confident Barack Obama voted in his home state of Chicago on Tuesday, as polls across the board predicted he will make history by being elected America's first black president. The Democratic candidate's Republican rival John McCain has defiantly promised an underdog upset in the election.

Obama was accompanied at the ballot by his wife Michelle, a strong presence in a marathon two-year campaign, and his two daughters, Malia and Sasha.

Obama arrived at the polling station, pausing to explain the process to his daughters at the booth, and prompting television commentators to joke: "Is he undecided?"

Obama, 47, who would be the first African American president in U.S. history if elected, was the strong favorite heading into Tuesday's vote.

McCain, accompanied by his wife Cindy, cast his ballot at the Albright United Methodist Church in Phoenix, Arizona before preparing to fly to Colorado and New Mexico, two battleground states he would likely need to score an upset victory. He gave supporters a thumbs-up sign and was in and out of the polling place within minutes.

"I'm very happy with where we are," McCain told ABC television's Good Morning America in an interview hours before polls opened. "We always do best when I'm a bit of an underdog."

"Look, I know I'm still the underdog, I understand that," McCain later said. "You can't imagine the excitement of an individual to be this close to the most important position in the world, and I'll enjoy it, enjoy it. I'll never forget it as long as I live."

Obama and McCain, separated by 25 years and a seemingly unbridgeable political gulf, had agreed on one thing during the longest presidential campaign in U.S. history - their promise to slam the door on the era of George W. Bush.

But they were deeply at odds over how to fix the nation's crumbling economy and end the 5 1/2-year war in Iraq, the issues that sent Bush's job approval rating plummeting to a record low at the end of his 8-year presidency.

Record numbers of Americans were expected at polling stations across the U.S., adding their ballots to 29 million citizens who had already voted in 30 states. The early vote tally suggested an advantage for Obama, with official statistics showing that Democrats voted in larger numbers than Republicans in North Carolina, Colorado, Florida and Iowa. All four states voted for Bush in 2004.

Democrats also anticipated strengthening their majority in the House of Representatives and in the Senate, although Republicans battled to hold their losses to a minimum and a significant number of races were rated as tossups in the campaign's final hours.

"I'm feeling kind of fired up. I'm feeling like I'm ready to go," Obama told nearly 100,000 people gathered for his final rally Monday night in Manassas, Virginia, near the site of the first major battle of the American Civil War that ended slavery.

"At this defining moment in history, Virginia, you can give this country the change it needs," Obama said to voters in a state that has not voted for a Democratic presidential nominee in 44 years. He later flew home to Chicago.

The Illinois senator's final full day of campaigning was bittersweet: he was mourning the loss of his grandmother, Madelyn Payne Dunham, 86, who helped raise him but died of cancer in Hawaii late Sunday and never got to see the results of the historic election.

"She's gone home," Obama said, tears running down both cheeks as tens of thousands of rowdy supporters at the University of North Carolina-Charlotte grew silent as he announced Dunham's death. The family said a private ceremony would be held later.

Obama came up a winner in two small New Hampshire towns, where a tradition of having the first Election Day votes tallied lives on. Obama defeated McCain by a 15-6 vote in Dixville Notch, while Hart's Location reported 17 votes for Obama, 10 for McCain and two for write-in Ron Paul. Bush carried both towns in the last two elections.

McCain, a 72-year-old four-term Arizona senator, ended the contest Monday with a frantic and grueling dash through several traditionally Republican states still not securely in his camp or even leaning to Obama.

McCain stopped in Florida, Virginia, Indiana, New Mexico and Nevada. And he again passed through Pennsylvania, the only state that voted Democratic in 2004 where he still hoped for a win.

He sought to raise fears among Americans that the Democratic nominee was outside the American mainstream, saying Sen. Obama is "in the far left lane."

As he sought to distance himself from the unpopular Bush, McCain stressed he was deeply at odds with White House economic policies while promising to clean house in the capital after years of scandal.

McCain said he sensed an upset in the making even though national and key state polls showing him trailing Obama.

"This momentum, this enthusiasm convinces me we're going to win tomorrow," McCain told a raucous evening rally in Henderson, Nevada.

He closed out the endurance test past midnight at a home-state rally in Prescott, Arizona. Obama ran television commercials in Arizona in the campaign's final days after polls showed the race tightening.

Both candidates were campaigning to the very end. Obama planned a quick campaign stop in Indiana on Election Day before a massive outdoor rally in front of the skyline in his adopted hometown of Chicago. McCain planned events Tuesday in Colorado and New Mexico, then a party at the Biltmore Hotel in Phoenix.

On election eve, the 47-year-old Obama, a first-term senator from Illinois, was favored to win all the states Democrats captured in 2004, when Bush defeated Democratic Sen. John Kerry. That would give him 251 electoral votes.

He was leading or tied in several states won by Bush, giving him several paths to the 270 vote threshold - such as victories in Ohio or Florida, or in a combination of smaller states.

McCain, meanwhile, must hold as many Bush states as possible while trying to capture a Democratic stronghold, such as Pennsylvania.

While no battleground state was ignored, Virginia and Ohio, where no Republican president has ever lost, seemed most coveted. Together, they account for 33 electoral votes that McCain must win.

Obama sprinted into the lead after economic concerns overwhelmed the war in Iraq, as the primary concern among voters.

Even though Republican experts argued the race was tightening, several polls suggested Obama's lead was growing.

A USA Today/Gallup poll published Monday found likely voters nationwide favoring Obama by 11 points over McCain, 53-42 percent, with a margin of error of 2 percentage points. Other polls showed Obama with a 7 or 8 percentage-point lead.

Polls conducted by Quinnipiac University showed Obama with significant leads in two critical swing states, Ohio and Pennsylvania, and tied with McCain in Florida, where the prize is 27 electoral votes. A win for Obama in any of these three states would be hard for McCain to overcome.

The American presidential election amounts to separate contests in the 50 U.S. states plus Washington, D.C. At stake are 538 electors, with the winning candidate needing to capture at least half plus one. Electors are apportioned to the states roughly according to population.

McCain's running mate, Alaska Gov. Sarah Palin, raced through five states - Ohio, Missouri, Iowa, Colorado and Nevada - in an effort to boost conservative turnout for McCain.

Delaware Sen. Joe Biden, Obama's running mate, campaigned in Missouri, Ohio and held a late night rally in Pennsylvania.

Obama has benefited from an astounding record fundraising effort and capitalized on a U.S. demographic shift as more young and non-white voters enter the electorate.

The Republicans have tried to curtail Obama's surge, dubbing him too inexperienced, too liberal and too tainted by associations with the political left to trust with the presidency. The message appealed to core Republican voters, but appears to have failed to convince a significant number of Democrats and independents.

Despite his lead in the polls, Obama urged his supporters against overconfidence. "Even if it rains tomorrow, you can't let that stop you. You've got to wait in line. You've got to vote, he said."