WASHINGTON — In the Boston-area home of a wealthy hospital executive one Saturday evening this month, President Obama departed from his usual campaign stump speech and offered an explanation as to why Democrats were seemingly doing so poorly this election season. Voters, he said, just aren’t thinking straight.

“Part of the reason that our politics seems so tough right now, and facts and science and argument does not seem to be winning the day all the time, is because we’re hard-wired not to always think clearly when we’re scared,” he told a roomful of doctors who chipped in at least $15,200 each to Democratic coffers. “And the country is scared, and they have good reason to be.”

The notion that voters would reject Democrats only because they don’t understand the facts prompted a round of recriminations — “Obama the snob,” read the headline on a Washington Post column by Michael Gerson, the former speechwriter for President George W. Bush — and fueled the underlying argument of the campaign that ends Tuesday. For all the discussion of health care and spending and jobs, at the core of the nation’s debate this fall has been the battle of elitism.

Mr. Obama’s remark that autumn evening played into a perception promoted by his critics that he is a Harvard-educated millionaire elitist who is sure that he knows best and thinks that those who disagree just aren’t in their right minds. Never mind that Mr. Obama was raised in less exalted circumstances by a single mother who he said once needed food stamps. Or that although he went to private school, he took years to pay off his college loans. Something about Mr. Obama’s cerebral confidence has made him into a symbol of something he never used to be.