The Republican chairman of the committee, Senator Richard C. Shelby of Alabama, prefers to note Mr. Mulvaney’s presence in the room — “He was there,” he said after one meeting — before pivoting to the importance of having Mr. Mnuchin doing the talking.
Wall Street analysts are also watching Mr. Mulvaney warily. Henrietta Treyz, the economic policy director at Veda Partners, a market analysis firm outside Washington, wrote in a note to clients this week that the threat of a presidential veto and Mr. Mulvaney’s hawkish views were the most significant risks to a deal falling apart.
In contrast, Mr. Mnuchin, a former Goldman Sachs banker and Hollywood film producer, tends to be the Trump administration’s voice of moderation, willing to compromise to reach a deal. Last month, Mr. Mnuchin emerged from a meeting in Ms. Pelosi’s office to tell reporters that the White House was not looking for a shutdown fight or flirting with a debt limit default. Mr. Mulvaney stood, red-faced, to his left, waiting for a chance to interject.
When the Treasury secretary stopped speaking, the acting chief of staff jumped in, charging Ms. Pelosi with having raised her spending demands and asserting — incorrectly — that she had promised to raise the debt ceiling no matter what, a shift, he insisted, from her previous position.
“I shouldn’t even be engaged in a conversation that has him mischaracterizing,” Ms. Pelosi later said.
By no means has Mr. Mulvaney been completely shut out: A White House official said that on Tuesday, Mr. Mulvaney participated in a meeting with the president about the debt ceiling. And two administration officials said that Mr. Trump’s lack of interest in the talks meant that the acting chief of staff could dip in and out of the discussions, sticking to the big picture without getting sucked into the minutiae.
At times, he has privately expressed bemusement at what he calls Mr. Mnuchin’s naïveté when it comes to haggling with Congress. In the spring, when Mr. Mnuchin suggested that House Democrats would be amenable to a “clean” raising of the debt ceiling — without preconditions, like raising the spending caps — Mr. Mulvaney insisted that Ms. Pelosi would surely try to extract concessions — as he would have.