On foreign conflicts, too, Democrats overwhelmingly expressed more faith in the decision-making of Mrs. Clinton, a former secretary of state, than of Mr. Sanders, a longtime antiwar figure.

“She knows all the players, all the world leaders,” Jan Lyles, 52, a consultant in Reno, Nev., said in an interview after the poll was completed. She added, approvingly, “She has her husband behind her for advice.” Three-quarters of Democrats view Bill Clinton favorably.

But support for Mrs. Clinton lags in some groups of Democratic primary voters, particularly men and younger voters. Among the misgivings is one that has surfaced before in her political career: Fifty-two percent of Democratic primary voters think that Mrs. Clinton says what she actually believes, compared with 62 percent who think Mr. Sanders is genuine in his remarks.

“It’s not so much I don’t trust her, but she seems to me to say what she thinks people want to hear,” said Jack Bernblum, 68, a self-employed Democrat from East Haven, Conn., who is leaning toward Mr. Sanders. “She has recently said something about legalizing marijuana, which is a brand new position for her. I don’t think she means anything she says.”

For Mr. Sanders, who is attracting bigger crowds than Mrs. Clinton and is running notably close to her in fund-raising, the overarching challenge is to transform an insurgent primary campaign aimed at two must-win states, Iowa and New Hampshire, into a formidable movement with broad national appeal. He will face his greatest test yet on Saturday night at the second Democratic debate, which will be televised nationally from Des Moines. Nearly half of Democratic primary voters say they are very likely to watch the debate, and an additional three in 10 said they were somewhat likely.