Once Mr. Biden hung up, Representative Joe Neguse, Democrat of Colorado and a member of leadership, reached out to Ms. Murphy and the moderate lawmakers to discuss the details of the statement. He was soon heading to Ms. Murphy’s office with a few colleagues, including Representative Jimmy Gomez of California, who was previously tapped by Ms. Pelosi for negotiations; Representative Mondaire Jones of New York, a freshman; and Mr. Pocan, a former head of the Progressive Caucus who once accused some of the moderates of child abuse during a heated debate over border aid.
After weeks of polarized meetings where moderates and progressives were hosted separately at the White House, it was one of the few times when the factions had met together. Lawmakers hunched over a laptop in Ms. Murphy’s office to edit what would ultimately be a 123-word statement, debating the semantics, down to the minute differences between terms like “voting for” and “support.” They haggled over whether to set a specific date for a vote to reassure progressives that the social policy bill would not be held up for long, settling on the week of Nov. 15.
“We act like we’re enemies and we’re not — we should have been sitting down talking to each other well before this,” said Representative Kathleen Rice, Democrat of New York and a close friend of Ms. Murphy. “It came to both of us saying that.”
Ms. Pelosi, who had staked her personal reputation on passage of both pieces of legislation, kept tabs on the talks from afar, filling lawmakers’ voice mailboxes with stern messages exhorting them to get in line behind the infrastructure bill and plucking updates from loyalists as they ducked in and out of private meetings.
The shuttle diplomacy gained urgency as the day wore on. At one point, Representative Sara Jacobs, a freshman Democrat from California, took off her shoes to run through the marble hallways, ferrying messages between leaders and representatives huddling in the Longworth House Office Building across the street. And ultimately, the joint statement — issued from personal Twitter accounts — was enough to secure the votes needed to pass the infrastructure bill the next morning, and the social policy measure before Thanksgiving.
For the lawmakers who helped broker the deal — several of whom are widely seen as likely candidates to lead the party in years to come — it was a validation of their ability to bridge internal divides, and a reminder that sometimes the best solutions come from the bottom up.
“Going forward,” Ms. Rice said, “it’s going to be hard for rank-and-file members not to be heard.”
Catie Edmondson contributed reporting.
