“I don’t think that having institutional knowledge is a bad thing per se,” she said in an interview. “I’m the youngest member of leadership. I’m still in my 40s. We need diversity in our leadership that appeals to a broad base of voters, and I think I do that.”

Others may still jump into the race. Much will depend on what happens in November, when a long list of new Democrats are likely to be elected. The party has decided to hold its leadership elections on or after Dec. 5 — later than usual, which could prolong the divisive battle for control but allow new coalitions to form that would guide the party into 2019.

If Democrats do not take the majority back, “there is an entirely new leadership team — no question about it,” said Representative John Yarmuth, Democrat of Kentucky, who is backing Ms. Sánchez for caucus chairwoman. “If we take the majority back, it’s going to be a fascinating dynamic, and I have no real way to read it.”

For her part, Ms. Pelosi insists that she is not going anywhere. “Aug. 18 of next year is the 100th anniversary of women having the right to vote,” she said in a brief hallway interview in the Capitol. (She was off by a year; the 100th anniversary is in 2020.) “At that time, we will have a hugely overwhelming record number of women in Congress, and we will have a woman speaker of the House.”

Yet an increasing number of Democrats running for Congress are promising voters they will not support Ms. Pelosi for either speaker or minority leader, which complicates her chances. Mr. Moulton said Democrats would be better off heading into the elections if Ms. Pelosi made a commitment beforehand to step down.

Ms. Pelosi has dismissed Mr. Moulton as “inconsequential.”

Beyond Ms. Sánchez and Ms. Lee, other Democrats are making their intentions known — and sometimes not so coyly.

“I want to be in leadership,” declared Representative Cheri Bustos, Democrat of Illinois, though she would not be more specific. Ms. Bustos, a centrist who beat her Republican opponent by 20 percentage points in a district won by President Trump, says Democrats are going to have “change in our leadership structure” no matter which party wins the House. She wants her perspective represented.