“Everybody wants leaders,” she said in an interview in her office at the Capitol, during which she was often as dismissive of critics in her own party as she was of the Republican opposition. “Not a lot of people want to be led.”

The Democrats’ loss on Tuesday in the special House election in Georgia illustrated how she has become a lightning rod for conservative attacks. Millions of dollars of ads in a red-tinted suburban Atlanta district linked Ms. Pelosi to a candidate, Jon Ossoff, who had not even committed to supporting her as party leader.

With the Clintons and former President Barack Obama in retirement, Ms. Pelosi, the well-known former House speaker, is vital to Republicans as the embodiment of liberalism: She lives in San Francisco, comes from a politically connected background and a wealthy household, and pushed through the Affordable Care Act, all of which plays right into the hands of most Republican candidates running between the coasts. On Thursday, renewing a long-running conservative trope about how much Republicans value her as a foil, Mr. Trump tweeted that he hoped Democrats “do not force Nancy P out.”

To many Democrats, Ms. Pelosi is their own indispensable woman, a legislative genius, tactical wizard and prolific fund-raiser whose ability to hold together a fractious caucus is written in her own success in passing many laws, and blocking even more.

But some in her caucus have reached a different conclusion: She is not, well, worth it.

Representative Kathleen Rice, Democrat of New York, said flatly that Democrats had lost their way and could not win the majority back with Ms. Pelosi leading the party. Ms. Rice hosted a Thursday afternoon meeting of just over a dozen anti-Pelosi House Democrats, according to Representative Tim Ryan of Ohio, who attended. The would-be coup plotters did not emerge with “any action items,” Mr. Ryan said.