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There's a theory making the rounds about Barack Obama. It goes like this:

The Illinois senator wins in states, such as Mississippi, that have a lot of black people in them, because black Americans overwhelmingly support his campaign.

He also wins in states that have very few black people, such as Nebraska, because white Americans in those states have no strong feelings about black Americans.

But in states with sizable black and white populations living together in industrial cities, such as Ohio and Pennsylvania, Mr. Obama loses, because too many working class whites won't vote for a black man.

The results in Pennsylvania suggest there is at least some truth in this sad hypothesis.

Exit polls from Tuesday's primaries show that 90 per cent of blacks but only 37 per cent of whites voted for Mr. Obama.

Even more ominous, about one-fifth of those who voted said race was a factor in this election, and about 40 per cent of those voters said they would not vote for Mr. Obama if he won the nomination.

We can't know how many voters lied to the exit pollsters - saying race was not an issue, when in their heart they knew it was; or insisting they would vote for Mr. Obama if he won the nomination, when secretly they doubted they would.

We can only know that in certain states with large, white, working and lower-middle class populations, Barack Obama can't seal the deal.

Yet it's more complex than "won't vote for a black man" or, for that matter, "won't vote for a woman."

Nathaniel Persily, a professor of law and political science at Columbia University, observes that the voting spectrum is more subtly shaded. While "there is certainly a subset of the population that will not vote for either candidate based on their individual immutable characteristics," he said, there are all sorts of others who are attracted to these candidates because of those characteristics.

There are the black voters who are coming out to the polls for the first time because Mr. Obama represents the first real hope that one of their own could become president. There are young voters who are getting involved in politics for the first time, fired-up by Mr. Obama's political crusade.

There are working-class women who support Hillary Clinton for the same reason, and with the same fervour, that blacks support Mr. Obama. And then there are the independents and even Republicans who are drawn to the Democratic Party this year, attracted by its energy, enthusiasm and opposition to the war in Iraq.

The question, then, is whether Mr. Obama or Ms. Clinton can bring more voters into the party than they drive out, simply because of their race or gender.

The other question, Prof. Persily believes, is what will happen to those "won't vote for a black" or "won't vote for a woman" Democrats, once the nominee is finally chosen.

"The relevant question for the fall is whether those voters are going to come back to the Democratic Party, whether they're not going to vote at all or whether they're going to vote for [Republican candidate John] McCain," he said.

It should also be pointed out that Mr. Obama's remarks about embittered rural voters did nothing to endear him to white rural and low-income voters. It would be deeply unfair to attribute racist motivations to voters who might have rejected Mr. Obama because of his own ill-chosen words.

Mr. Obama observed yesterday that he actually improved his standing among white voters in Pennsylvania over Ohio. If he can improve it further in Indiana, May 6, then the race card may be put back into the deck, at least for now.

Then again, the campaign doesn't seem optimistic about its chances with this demographic. "The white working class has gone to the Republican nominee for many elections, going back even to the Clinton years," David Axelrod, Mr. Obama's chief adviser, explained to National Public Radio Wednesday.

"This is not new that Democratic candidates don't rely solely on those votes."

That is not an attitude that is likely to attract white middle America to Mr. Obama's campaign. And unless Mr. Obama improves his performance among this group, his critics will continue to question whether he could prevail in the general election.

The legacies of the civil-rights era - busing, race riots and ghettoization - are not easily erased. But there is good evidence that the generation born after the 1960s is more comfortable crossing the racial divide, even as rising incomes among blacks help to erase it.

In 1960, John Kennedy proved "won't vote for a Catholic" was not fatal to presidential prospects. Whether 2008 puts "won't vote for a black" to rest, we just can't know.