“I like Ben Carson because he’s not government, and I’m tired of government,” said Doug May, 70, a retired chief information officer in Bluffton, S.C. Mr. May added, referring to the Russian president, Vladimir V. Putin: “What worries me the most about Donald Trump is what he would do if put into a situation where he is sitting down with Putin. With his mouth, I have no idea what he would say to people.”

Democratic voters seem more enthusiastic about Mrs. Clinton as the party’s possible nominee than Republicans do about Mr. Trump. Forty-eight percent of Democrats said they would support her enthusiastically, and 35 percent of Republicans said the same of Mr. Trump.

In the face of growing dissatisfaction among voters over all for Mrs. Clinton’s explanation about using a personal email server as secretary of state, female Democrats are starting to fall away — and male party members even more so. Thirty-nine percent of male Democrats now support her, down from 53 percent, and 54 percent of Democratic women backed her compared with 61 percent in August. One-quarter of Democratic voters said they were mostly dissatisfied with her explanations on the email issue.

While Democrats give Mrs. Clinton high marks for leadership, her rating on honesty and trustworthiness has fallen 10 percentage points from August, to 64 percent. Long the choice of a majority of Democrats, Mrs. Clinton now draws support from 47 percent of them; Mr. Sanders improved his standing by 10 points, to 27 percent.

Mr. Biden’s theoretical support largely comes from people who would vote for Mrs. Clinton, the poll found; his strongest backers tend to be older and low-income and lack a college education.

John Kern, a 28-year-old Democrat from New Jersey who works in financial services, said he believed that Mr. Biden would be the strongest candidate to unify the party and appeal to cross-sections of voters in all regions of the country.