As Barack Obama makes his slow but steady way toward the Democratic nomination, the assumption in the admiring precincts of the press corps is that voters have dismissed as irrelevant his longtime association with the Reverend Jeremiah Wright. But that may prove as mistaken as the assumption, back in 1988, that voters would not be impressed by Michael Dukakis’s 11-year support of a law granting weekend furloughs to convicts sentenced to life without parole, an issue brought up in the primaries by Al Gore but largely ignored in press coverage at the time.

Evidence for this comes in the exit polls from the West Virginia and Kentucky primaries on May 13 and 20. In both, about half the voters — and these are voters in the Democratic primary — said that they believe Mr. Obama shares Rev. Wright’s views either somewhat or a lot. And slightly under 50% of these voters said that Mr. Obama is honest and trustworthy.

To be sure, these were primaries in which Mr. Obama was beaten, and beaten badly, by Hillary Clinton — 67% to 26% in West Virginia, 66% to 30% in Kentucky. So they would be inclined, one might believe, to think ill of Mr. Obama. Yet it is not universally the case that voters who choose one candidate in a hotly contested election doubt whether the other candidate is honest. You can oppose someone who you believe to be trustworthy. Only 38% of Americans voted for Barry Goldwater in 1964 and George McGovern in 1972. But probably a higher percentage believed that they were basically honest.

Which leads me to ask why these voters declined to say Mr. Obama is honest. When have they seen him lie or being caught in a lie? The response to the question on Rev. Wright may provide the answer. They know that he attended Rev. Wright’s church for 20 years. They know that he said, both on March 18 when he refused to renounce Rev. Wright and on April 29 when he did renounce him, that he was not aware of his pastor and spiritual mentor’s incendiary comments. Yet half of these voters also think that, despite those statements, Mr. Obama agrees with what Rev. Wright has been saying.

It’s a little dangerous in interpreting polls to assume that voters’ thinking proceeds along logical lines. People who aren’t professionally involved in politics, whose knowledge comes from bits and snippets of news, can hold beliefs that are contradictory or in tension with each other. They don’t feel obliged to resolve contradictions. But even granting that, it seems to me that about half of West Virginia and Kentucky Democratic primary voters were saying that Mr. Obama lied about not knowing what Rev. Wright has been preaching and that he agrees with him a lot more than he has let on.

Now West Virginia and Kentucky are not typical primary states. They, together with Arkansas, where Mrs. Clinton was first lady for 12 years, were Mr. Obama’s weakest states in this year’s primaries. And some percentage of registered Democrats in these states have been voting Republican in recent presidential elections. Nevertheless, the negative verdict these voters render on Mr. Obama’s honesty and his relationship with Mr. Wright is likely to be typical of some significant quantum of potential Democratic voters this year. And not just in states like West Virginia and Kentucky, which he will certainly lose, but in marginal states which he must carry in order to be elected.

I find confirmation from this in a recent focus group conducted for the Annenberg Public Policy Center by pollster Peter Hart (for whom I worked for seven years) of non-primary voters in Charlottesville, Va. As Mr. Hart and Alex Horowitz note in their analysis of reactions to Mr. Obama, “When asked to recount any two memories of the total presidential campaign so far, seven of the 12 participants cite Rev. Wright by name. So far, clips of Rev. Wright clearly are the one ‘key defining moment’ of this campaign.”

Most reporters are liberals, whose circles of friends and acquaintances have included people with views not dissimilar to those of Rev. Wright or William Ayers, the unrepentant Weather Underground bomber with whom Mr. Obama served on a nonprofit board and at whose house his state Senate candidacy was launched.

Such reporters don’t find these views utterly repugnant or particularly noteworthy. But most American voters do. And they wonder whether a candidate who associates with such people agrees with them — or disbelieve him when he says he doesn’t.

Though most in the press won’t admit it, that’s a problem — for the Obama candidacy and for the whole Democratic Party once it nominates him.