The road to the Democratic nomination would likely be fraught for any moderate, especially one who would not break a historic barrier by virtue of identity, as Barack Obama did in 2008. To some Democrats, a more centrist message might too closely echo Hillary Clinton’s unsuccessful 2016 campaign, which left many in the party determined to focus on mobilizing the left over pursuing the middle. And the most vocal Democratic factions have shown little interest so far in settling for something other than a liberal champion, on issues from taxation and business regulation to criminal justice and gender equality.

Ms. Warren has emerged as something of an intellectual pacesetter for liberal Democrats on economic issues, including her proposal to tax the wealth of households with assets greater than $50 million at a rate of two or three percent per year. And on Monday Ms. Harris, whose signature proposal has been a more conventional middle-class tax cut, called in a CNN interview for the elimination of private health insurance as part of a shift toward a “Medicare for all” single-payer health care.

Several other liberals of differing stripes are likely to join the race soon, including Senators Bernie Sanders of Vermont and Cory Booker of New Jersey; others are considering it seriously, like Senators Sherrod Brown of Ohio and Jeff Merkley of Oregon.

Polls of Democratic voters offer mixed signals about how liberal they want their nominee to be. There is no question the party has moved leftward: the Gallup Poll found this month that for the first time in decades, a majority of Democrats describe themselves as liberal, while just 34 percent now call themselves moderate. And taxing the rich is broadly popular, with a sizable majority of Americans believing wealthy people and corporations pay too little to the government.

“People have grown more liberal and more willing to call themselves liberal,” said Lydia Saad, a senior editor at Gallup, cautioning that ideology did not necessarily predict voting behavior: “The public is very fungible in terms of who they will accept as a leader, based on things that seem to go beyond ideology.”

Arkadi Gerney, a Democratic strategist who runs the Hub Project, a liberal advocacy group that has focused heavily on taxes, said that intensive issue polling had consistently found powerful support for raising taxes on the wealthy, not just among Democrats but also among working-class white voters in Mr. Trump’s base.