A growing faction of Democrats is pushing for their party to crank up the heat on their opposition to President Trump. Cooler heads say that more vitriol won’t capitalize on Republican struggles and offer a winning alternative. 

On Tuesday, President Biden accused Mr. Trump of “taking a hatchet” to Social Security and doing “damage and destruction” to it. Even the New York Times noted that Mr. Trump has “promised” not to cut benefits, so this is standard politicking for the Democratic old guard.

Vice President Harris focused on more ephemeral, darker themes rather than specific policies in remarks to party activists on Wednesday. This was more reflective of Democratic hotheads, a name that echoes the Copperhead faction of the party that resisted fighting the Civil War. 

Mr. Trump, Ms. Harris said, launched “the wholesale abandonment” of “America’s highest ideals” and his “is not a vision that Americans want.” Never mind that the president’s vision prevailed over hers in November, and Wednesday’s Emerson College poll found that she’d lose in a rematch.

Congressional Democrats fared even worse in Emerson, trailing Mr. Trump 40 percent to 32 percent on perceptions of who’d better deal with America’s problems. Many Democrats refuse to accept these realities, insisting that voters regret backing Mr. Trump and, therefore, the party doesn’t need to change. 

On CNBC Thursday, pollster Frank Luntz found no evidence to support this belief. Mr. Trump’s voters, the pollster said, will stick with him even if they’re “hurt economically.” A billionaire Illinois Democrat, Governor Pritzker, urged his party to test the theory by inflicting pain on Americans.

“Never before in my life,” Mr. Pritzker said in a speech on Tuesday, “have I called for mass protests, for mobilization, for disruption. But I am now.” He went further on Wednesday. “Republicans,” he said on MSNBC, “cannot know a moment of peace.” 

Mr. Pritzker lit into his party’s cooler heads for “simpering timidity” and said they had to “stop thinking we can reason or negotiate with a madman.” He invoked Nazi Germany and said that Republican portraits would hang in “museum halls reserved for tyrants and traitors.”

On Tuesday, Senator Schumer, the Democratic minority leader, tried speaking for the opposition. “Donald Trump’s first 100 days,” he said on the Senate floor, “can be defined by one big ‘F word’: Failure.” This rhetorical device — teasing profanity to titillate — marked the 74-year-old as a relic of a bygone, more genteel era.

Hotheaded Democrats don’t censor themselves when speaking of Mr. Trump. The disconnect may help explain why, in Tuesday’s CNN poll, Mr. Schumer was viewed favorably by just 14 percent of Democrats and Democrat-leaning independents under 35, though the divide isn’t defined by age.

Thursday’s poll by the Atlanta Journal-Constitution found “a collapse in favorability” for Democrats in Georgia “as liberal voters outraged by” Mr. Trump “demand a more confrontational pushback.” Just 35 percent of the state’s registered voters had a positive view of Democrats.

On Wednesday’s “Tara Palmeri Show,” the two factions clashed. President Clinton’s strategist, James Carville, faced the DNC vice chairman, David Hogg, who proposes spending $20 million to primary old-school Democrats.

“I think it is abominable,” Mr. Carville said, for “an official of a political party — that is being paid or supported by that political party — to go out and raise money to defeat members of the same party. I think that’s jackassery of the highest level.” 

“Carville,” Mr. Hogg said on CNN after the debate, “believes in a politics of being timid, of hiding. I believe in fighting.” It’s a sign of the hunger for red meat among the hotheads that they feel Mr. Carville, dubbed “the Ragin’ Cajun” in the 1990s, is too docile.

Democrats who want to offer a cooler contrast with Mr. Trump’s White House inferno are sure that the old ways win. But before they can get a shot at persuading voters, they’ll have to maintain control of the party — and that means breaking the fever of the hotheads first.

Anger. Vulgarity. Bullying. These are qualities that Democrats often ascribe to Mr. Trump. If they believe that caricature is accurate, Nietzsche’s advice holds true: Anyone “who fights monsters should see to it that he does not become a monster himself.”