In those discussions, Mr. Portman, who was President George W. Bush’s budget director, helped drive the policy discussions for Republicans, while Ms. Sinema wrangled the group’s meetings and helped keep their focus on the issues on hand.

“They have a good relationship with one another, and in a relationship that is built on trust,” Senator Susan Collins, Republican of Maine, said of the pair in an interview.

In order to finalize the agreement, the senators ultimately splintered into small working groups, each tasked with hammering out different aspects of the bill, including transit and broadband projects, and financing provisions.

While at her birthday dinner last Saturday night, Ms. Sinema was on a call with Senators Jeanne Shaheen, Democrat of New Hampshire, Lisa Murkowski, Republican of Alaska, and Ms. Collins, reconciling a series of accounting figures about unspent pandemic relief money, a key financing mechanism, Ms. Collins recalled. (Having nicknamed the four senators “the Wonder Women,” Ms. Sinema gifted the other three stemless wine glasses with the superhero’s logo.)

Mr. Portman spent nine hours on Tuesday in his conference room in the Russell Senate Office Building with Steve Ricchetti, the White House counselor, wrestling with how to resolve remaining issues, including transit funding.

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