But Patrick Murray, the director of Monmouth’s Polling Institute, who recently spent time in Iowa, said those numbers did not give the full picture of Mr. Biden’s support in the state.

“I did not meet one Biden voter who was in any way, shape or form excited about voting for Biden,” Mr. Murray said. “They feel that they have to vote for Joe Biden as the centrist candidate, to keep somebody from the left who they feel is unelectable from getting the nomination.”

And JoAnn Hardy, the Democratic chairwoman of Cerro Gordo County, Iowa, where most of the Democratic candidates recently attended the gathering known as the Wing Ding dinner, attributed Mr. Biden’s lead in part to simply being well-known.

“He’s doing O.K., but I think a lot of his initial strength was name recognition,” she said. “As the voters get to meet the other candidates, he may be surpassed soon. I would not be surprised.”