“We want to remove all doubt to how we go forward in a way that puts our best foot forward on Day 1, in order to show that we can govern,” she said, according to one person present, adding, “Make your fight, make your case, but not every fight is the last fight.”

Ms. Pelosi, however, is a skilled navigator of turbulent waters. During the campaign, she resisted calls from progressives to support the movement to abolish Immigration and Customs Enforcement and pushed back against efforts from the left to engage President Trump tit for tat on divisive issues like immigration.

But after an election in which Democrats made considerable gains in districts won by Mr. Trump, the prospect of a crop of outspoken progressives having outsize power and influence in a newly realigned Washington is worrying some of the more pragmatic Democrats, especially those who flipped Republican seats this month.

“For me and for any of the others in these red-to-blue seats, we’re in a position that if we ever want to hold onto these seats — and we’re the ones who delivered the majority — then we have to be able to go back to our districts and show that we’ve accomplished something,” said Katie Hill, an incoming freshman from California, who strongly backs Ms. Pelosi.

“If we’re going to be strong as a majority, we need to be cohesive as much as possible,” Ms. Hill said. “We can’t be like the Republicans and the Tea Party.”