Ms. Jean-Pierre faulted several Democratic candidates for parroting Republican attacks on their own party, rebuking former Gov. John Hickenlooper in particular for raising the specter of socialism on the debate stage Thursday night.

“We should be saying, ‘We are the party trying to come up with big solutions to fix the damage this president has done,’” Ms. Jean-Pierre said.

Indeed, liberal activists are growing increasingly irritated about the tendency of some party leaders to view issues through the prism of how they will play with mostly white moderate and center-right voters.

“Sometimes appealing too much to Joe in the diner means you’re not reaching Joanna in an apartment building in an urban core,” said Brittany Packnett, a social justice organizer. “We need to engage people who have been forgotten about by establishment politics and help them recognize they have a role to play as citizens.”

In some respects the Democrats’ position resembles that of the Republican Party in the early stages of the 2012 and 2016 presidential elections, when a jumble of candidates crowded into televised debates, shoving each other toward their party’s ideological pole on some of the same issues — immigration, health care and abortion rights.

Most of the 2020 presidential candidates who dominated the recent debates were aiming directly at voters on the left. There were few appeals to the political center or pleas about the electoral perils of left-wing politics. With few exceptions, the moderate candidates on stage spoke in tones so gentle they verged on apologetic, seeking to nudge the party away from far-left ideas without confronting them head-on.

Senator Amy Klobuchar of Minnesota, perhaps the best-known moderate in the race besides Mr. Biden, did not dwell in the Wednesday debate on her strong objections to pursuing a “Medicare for all” health care policy. Instead, she diplomatically suggested Democrats adopt a different “bold idea” — the less disruptive policy of creating an optional government plan.