The results signal how Mr. Biden and Mr. Sanders, two longtime politicians on opposite ends of the party’s ideological spectrum, are entering the race with great familiarity to voters. It remains to be seen if that will translate to hardened support, particularly in one of the largest, most wide-open and diverse Democratic primary fields in history.

The next closest figure to Mr. Biden and Mr. Sanders, according to the poll, was Senator Elizabeth Warren of Massachusetts, who was among the first to announce her presidential candidacy. Ms. Warren was the top choice for 9 percent of respondents, followed by Senator Kamala Harris of California, who was favored by 7 percent of respondents and had soaring favorability ratings.

Other candidates — including Senators Cory Booker of New Jersey, Kirsten Gillibrand of New York and Amy Klobuchar of Minnesota — have struggled to make an imprint, the poll found.

The poll also asked respondents about their policy priorities, offering a hint of the political leanings of the Democratic electorate as the party wrestles with its ideological core. Progressive ideas such as raising taxes on the wealthiest Americans, the bold climate action known as the Green New Deal, and a “Medicare for all” health care system all enjoyed widespread support among likely caucusgoers.

This comes even as most voters preferred Mr. Biden, who has billed himself as a moderate opposed to the Democrats’ leftward lurch.