Two weeks after dinner at Ms. Murkowski’s, they honed the initial $908 billion framework over slices of pizza in a large Senate hearing room and rushed to arrange a news conference for the next morning. They moved so quickly that the posters Mr. Manchin had ordered were not done by the time the event began.

“None of us thought in good conscience we could go home for Christmas with all these people thrown out of their apartments, closing their businesses, getting into food lines,” said Mr. Warner, a Virginia Democrat. “It would be the ultimate Scrooge-like activity.”

The moderates did not know it, but Democratic leaders had been doing their own postelection recalibration after insisting for months that any deal less than $2 trillion was inadequate.

Three days after the dinner at Ms. Murkowski’s house, Speaker Nancy Pelosi and Senator Chuck Schumer, Democrat of New York and the minority leader, had driven to Wilmington to meet with Mr. Biden and plan the year ahead. The president-elect’s message was plain.

“He knew we could not get everything now, but anything we could get would make his job easier when he became president,” Mr. Schumer said. “We agreed.”

When the moderates introduced their plan, the top Democrats saw their opportunity. They quickly embraced it as the easiest vehicle for jump-starting negotiations.

It was a major shift for the leaders, who had rejected Trump administration proposals twice as large, refusing to budge as the election approached even as they privately conceded that there was little momentum for a deal. During one call in late September, Ms. Pelosi had told Treasury Secretary Steven Mnuchin that she had spent a sleepless night watching a rerun of “The Princess Bride,” the 1987 cult classic. She compared their negotiations to how Billy Crystal’s character, Miracle Max, describes a patient in the film who has been tortured to the brink of death, pronouncing them “mostly dead.”