But Lee Kujawa, 72, of Wauwatosa, Wis., near Milwaukee, made a case for Mr. Biden, seeing him as “the most electable.”

“He can stand up to Trump,” said Mr. Kujawa, who said he believed the party would not pay a penalty by nominating its first white man since John Kerry in 2004. Referring to Mr. Biden, he said, “He could pick Kamala Harris as a running mate; she’s one of my top three favorites.”

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White men have largely ruled both the Democratic and Republican parties throughout American history, even as they have declined to roughly 30 percent of the population, and many voters still have preconceptions of presidents as white and male. Mr. Biden and Mr. Sanders are starting off with other advantages as well: They are the best-known candidates at this stage, both with experience running for president, and they are well positioned to have the money and resources to compete through the 2020 primaries.

But as older white men, they are out of step with ascendant forces in the party today.

Women, minorities and young people are fueling much of its energy, and they are well represented by multiple well-qualified, politically savvy female and nonwhite Democrats who are running. Ms. Harris in particular has had a strong start in fund-raising, and only Mr. Biden and Mr. Sanders consistently outpace her in polls.

The party also has a new primary calendar for 2020 that could help these candidates: The diverse Democratic electorates in California and Texas will vote earlier than usual, and candidates like Ms. Harris and Mr. Booker could also benefit from the sizable black vote in the early primary state of South Carolina.