Mr. Mulvaney, who led the debt ceiling brinkmanship in his previous job as a Republican representative from South Carolina, explained last week that he would like to see concessions such as spending cuts or budget process changes tied to any bill that would raise the debt ceiling. But Steven Mnuchin, the Treasury secretary, has urged Congress to raise the borrowing limit as quickly as possible, with no strings attached, to avoid roiling financial markets and putting the economy at risk.
While the administration has not taken an official stance, President Trump signaled in a meeting with the Republican leadership this week that Mr. Mnuchin, not Mr. Mulvaney, was leading debt ceiling negotiations.
Steve Bell, a former Republican staff director of the Senate Budget Committee, said the party’s difficulties raising the debt limit were emblematic of its current state of dysfunction.
“This is the reality of the Balkanization of the Republican Party,” said Mr. Bell, now with the Bipartisan Policy Center. “It is almost theological, and this is not something that is going to cement the party back together.”