Correction: An earlier version of this story incorrectly stated that an incumbent president has never won re-election after a majority of the electorate voted to throw him out. President Bill Clinton did not win a majority in a three-way race, although he did win the most votes. The story has been corrected.

Most polls at this moment suggest GOP nominee Mitt Romney is in the lead nationally, but surveys in the nine or so swing states are registering a narrow advantage for President Obama.

So here’s a prospect worth contemplating: What if Romney carries the popular vote, but Obama regains the presidency by winning 270 votes or more in the electoral college?

“I think it’s a 50/50 possibility — or more,” said Mark McKinnon, who was a political strategist for President George W. Bush.

“If the election were held tomorrow, it wouldn’t just be a possibility, it would be actual,” added William A. Galston, a senior fellow at the Brookings Institution, who also served as a policy adviser to President Bill Clinton.

That kind of split decision between the electorate and the electoral college would mark the fifth time in American history — and the second time in a dozen years — that the person who occupies the White House was not the one who got the most votes on Election Day.

Explore the 2012 electoral map and view historical results and demographics

No incumbent president seeking a second term has ever won the electoral college and lost the popular vote.

Every modern president to be reelected — Dwight D. Eisenhower, Richard M. Nixon, Ronald Reagan, Clinton, George W. Bush — has gotten a bigger share of the vote in their second bid for office than their first, and with it, a chance to claim a mandate. (Though Clinton got more votes than his first race and won in the electoral college, he was re-elected in 1996 without winning a majority in a three-way race against Republican Bob Dole and independent Ross Perot.)

A win in the electoral college that is not accompanied by one in the popular vote casts a shadow over the president and his ability to govern.

If Obama is reelected that way, “the Republican base will be screaming that Romney should be president, and Obama doesn’t represent the country,” McKinnon predicted. “It’s going to encourage more hyperpartisanship.”

Veterans of the Bush White House understand that problem well. Bush was never able to shake the accusations of some Democrats that he had “stolen” the 2000 election in a recount of Florida votes that required a U.S. Supreme Court decision to determine the winner. Then-Vice President Al Gore had won the popular vote that year by 500,000 votes.

“A close election is a polarizing event, and a discrepancy between the popular outcome and the electoral vote only adds to the polarization,” said Karen Hughes, who served as a counselor to Bush. “It rubs a raw nerve even rawer.”

And that kind of split decision may well happen more often in the future, if the nation’s political system remains both deeply and closely divided.

Polarization amplifies the quirkiness of the electoral college system by encouraging the candidates to ignore the nation’s biggest population centers, except for fundraising purposes, and to devote their energies to winning over that narrow slice of voters who live in states where the Election Day outcome is in doubt.

The electoral college is an artifact of an era when the lack of organized political parties and the difficulties of travel and communication prevented candidates from waging a national campaign.

Given those impediments, the Founding Fathers were leery of a direct popular vote as a means of gauging the popular will. But they also did not want to give Congress the power to select a president. So they set up a process by which each state would be allocated a number of electors, equal to the total of its House members and senators.

If that system yet again produces a president who does not also win the popular vote, it will raise new questions about whether the electoral college should be abolished — something that would require a constitutional amendment.

For now, however, both campaigns are so fixated on winning the battleground states that they are not giving much thought to the prospect of an electoral college victory that is not accompanied by a popular-vote mandate.

Obama’s strategists, for instance, say they have not conducted a single national poll and have had no conversations about how to deal with the political fallout from a split decision.

However, the Obama campaign this week began airing an ad in the battleground states reminding voters of the trauma of the 2000 Florida recount that awarded its electoral votes — and the presidency — to Bush.

Ironically, Gore’s campaign had actually been bracing for the opposite outcome that year, recalled Tad Devine, who was a top strategist for the Gore campaign.

Bush had such a huge lead in his home state of Texas that Gore’s team figured that state alone would add a percentage point to his popular vote — and potentially put him over the top in the popular vote without giving him the electoral college.

That might also have been the case four years later, had Democratic nominee John F. Kerry succeeded in carrying Ohio, a state that is once again at the center of electoral college calculations.

In either instance, Devine said, “we would have claimed victory and said, ‘This is the Constitution.’ We wouldn’t have hesitated a second.”

Hughes recalled that Bush spent much of his early presidency trying to bind the wounds of the disputed 2000 election.

After the Supreme Court declared him the president-elect, the then-governor of Texas made his first speech from the Democratic-controlled chamber of the state House in Austin.

Once in Washington, Bush made a point of inviting Democrats such as the late Sen. Edward M. Kennedy (D-Mass.) to the White House for movie nights, and he celebrated the 100th day of his presidency by throwing a picnic on the White House lawn for members of Congress. One of his first big legislative initiatives was the No Child Left Behind education law, which won bipartisan support.

“We made those decisions very deliberately, as a sign of healing and to bring the country together,” Hughes said.

If one candidate carries the popular vote, but the other wins the electoral college tally, the prospects for a drawn-out recount are high in swing states where the results are close.

But an even bigger problem would arise after that, as the new president — whoever he is — tries to govern and forge consensus on how to tackle a host of major problems.

An election in which the popular will is thwarted is “the worst of all possible outcomes,” Galston said. “We are in a situation now where the government of the United States needs to regain its capacity to act after this election. We are facing some risks that are both serious and imminent.”