By Matthew Bigg

ATLANTA (Reuters) - For supporters of Democratic presidential candidate Barack Obama it is a nightmare scenario -- his apparent lead in the battle for the White House suddenly evaporates on Election Day. The cause? Race.

As Republican rival John McCain celebrates victory, it emerges that a small but decisive percentage of white voters who had declared to opinion pollsters they supported Obama actually chose differently in the privacy of the ballot booth.

With opinion surveys making Obama the favorite over McCain less than three weeks before the November 4 election, attention has turned to the question of how many white Americans might be lying to pollsters about their willingness to vote for a black president.

The phenomenon is known as the "Bradley effect," after Tom Bradley, an African American who narrowly lost the 1982 California governor's election despite leading in polls.

His defeat surprised observers who concluded many white voters had not been honest about their intentions. Ever since, pollsters have tried to factor in the Bradley effect in elections featuring black candidates.

Those concerns weighed heavily on John Estep as he canvassed for Obama last week in the mainly white town of St. Bernard, Ohio, where he was once mayor.

"They will say in a poll, or say on the porch, 'I'll vote for Obama.' But I question how many will stick with a person of color when they pull that (voting booth) curtain," said Estep.

"A lot will talk the talk but how many will walk the walk?"

Analysts counter that since the 1970s, surveys have shown a sharp decline in the number of voters who say they would not vote for an African American for president.

Recent surveys have indicated that Obama's race is less of an impediment to voters than McCain's age. At 72, McCain would be the oldest person to assume the U.S. presidency.

FACTORING IN RACE

The analysts also note that few people who are turned off by a black candidate's race would likely vote Democrat anyway.

"The ... South is where you have a long-standing tradition of racial polarization (in voting)," said Merle Black, professor of politics at Emory University in Atlanta. White voters in the South have for decades favored Republicans while black voters nationally side with the Democratic Party.

White Democratic presidential candidate John Kerry only gained 23 percent of the white vote in Georgia in 2004 and lost the state, evidence that white voters prefer Republicans for reasons of ideology rather than race, said Black.

Race is a sensitive subject in the United States because of the country's history of slavery and racial segregation, and continued social inequality between white Americans and black Americans, who form about 13 percent of the population.

Politicians rarely address it directly and both the Obama and McCain campaigns downplay the idea the some whites might not be speaking honestly about their voting plans.

The diversity of the U.S. electorate makes it hard to quantify the phenomenon, pollsters say. An older voter in South Florida may be of the same race as a young union member in Virginia or a businesswoman in Colorado but share little else.

The Democratic primaries in which voters in the states picked the party's presidential candidate painted a mixed picture of the potential for a Bradley effect. In some states, Obama got fewer white votes than expected but in South Carolina and elsewhere it was the opposite.

Commentator Earl Ofari Hutchinson said there was a potential for the Bradley effect to be decisive, and that Obama might need a 10 percent lead in opinion polls to be sure of overcoming it.

"The big question is, can the dire straits that the economy is in ... offset any penchant on the part of the white voters to lie to pollsters?" Hutchinson said.

"It depends on how deeply someone has racial bias (and if) that person feels that Obama can do something for him or her."

The latest Reuters/C-SPAN/Zogby poll gave Obama a 4-point national lead.

Pollster John Zogby said he took the prospect of overstating white support for Obama very seriously.

Zogby tries to factor any potential Bradley effect into his polling but said he believes it will be negligible, in part because estimates of Obama's support had proved accurate during the primaries.

Even so, Zogby added a note of caution, "I don't see it as a big factor but I may learn a lot on Election Day."

(Additional reporting by Andrea Hopkins in Ohio)

(Editing by Michael Christie)