WASHINGTON -- An uncertain four years could await President Barack Obama if, under one possible outcome of Tuesday's election, he clings to power despite losing the popular vote to Republican Mitt Romney.

Never before in U.S. history has a sitting president won a second term without winning the popular vote. This year, it's within the realm of possibility. A very tight race seems to favour Obama in the handful of most competitive states that will decide the winner, even if growing Republican enthusiasm means more voters overall go for Romney.

If that happens, Obama would face mounting problems -- stubbornly high unemployment, Mideast unrest, the "fiscal cliff" of tax increases and spending cuts in January -- with little ability to claim Americans support his way forward, political analysts say.

"If there's any room in these results for Republicans to say the public doesn't support what he's doing, it would make an already toxic, incredibly difficult situation that much worse," Princeton University historian Julian Zelizer said.

Call it Al Gore's revenge. In the 2000 election, the vice-president was denied the presidency despite winning more votes than President George W. Bush. Even after the Supreme Court settled the race, allegations of a "bloodless coup" deprived Bush of the clear mandate needed to unite a divided nation, until the Sept. 11, 2001, attacks united Americans against a terrorist threat.

A decade later, as a bitter election draws to a close, Americans are even more divided.

Four U.S. presidents have assumed office despite losing the popular vote, including Bush and John Quincy Adams, who in 1824 lost both the popular and electoral vote but was handed the election by the House of Representatives.

All of those elections involved non-incumbents seeking their first term. For a sitting president to lose the popular vote and yet remain the world's most powerful leader would be uncharted territory, raising difficult questions about our electoral system.

A look at the map makes it easy to see exactly how it could happen. Passions run high this year among Republicans, and turnout for Romney probably will be big -- especially in Southern states that he's likely to win. But last-minute polls show Obama clinging to a small advantage in a handful of battleground states like Ohio and Florida, which could enable him to block Romney's path to the requisite 270 electoral votes. Those votes are won state by state and decide the election.

"This is going to be a turnout election," Obama said Monday in a radio interview. "We've got the votes to win Florida. It just depends on whether people turn out or not."

If Obama marches to 270 but loses the popular vote, he would face the unpleasant prospect of spending four years as a president with little power. "Republicans would have a pretty strong hand to play against him," said Craig Robinson, the Iowa Republicans' former political director.

No politician wants to be relegated to irrelevance. Unshackled from Democratic donors and with his last election behind him, a second-term Obama could manoeuvr sharply toward the centre, seeking compromise with Republicans on major issues as did his Democratic predecessor, former President Bill Clinton. He might rethink his call for raising taxes on wealthier Americans to pay for deficit reduction, or pull back some environmental or business regulations in the interest of getting things done for the American people.

Such a move inevitably would anger the liberal base to which he owes his presidency, said Hank Sheinkopf, a Democratic strategist. But Obama may not have a choice.

"If you're on the way out the door and you're a 'lame duck,' offending people doesn't matter anymore," Sheinkopf said.

What matters is salvaging your legacy.

Americans remember the big, sweeping acts that define a generation. Think Mars exploration, a major climate initiative or a war on cancer, said Douglas Brinkley, a presidential historian at Rice University.

"President Obama will need to put his stamp on something large," Brinkley said. "Our country is dying for something that unites us."