A plurality of Republican voters, 47 percent, said they believed Mr. Obama, who was born in Hawaii, was born in another country; 22 percent said they did not know where he was born, and 32 percent said they believed he was born in the United States.

While that might indicate that there is a receptive audience for the real estate mogul Donald J. Trump as he raises questions about Mr. Obama’s citizenship, the poll also pointed to potential roadblocks for him should he pursue a formal candidacy.

Mr. Trump has been getting considerable attention as a possibly strong contender, but just about as many Republicans view him favorably as view him unfavorably — 35 percent favorably and 32 percent unfavorably— and nearly 60 percent of Republicans interviewed said they did not believe he was a serious candidate. (Far more of all voters view him unfavorably — 46 percent — than view him favorably, 25 percent.)

If one Republican stands out in the Times/CBS News poll, it is Mr. Huckabee, who has his own show on the Fox News Channel.