WASHINGTON — After weeks of discussions about his future, Zachary D. Fuentes, the 36-year-old deputy White House chief of staff, had a plan.

Mr. Fuentes told colleagues that after his mentor, John F. Kelly, left his job as chief of staff at the end of the year, he would “hide out” at the Eisenhower Executive Office Building, adjacent to the White House, for six months, remaining on the payroll in a nebulous role. Then, in July, when he had completed 15 years of service in the Coast Guard, Mr. Fuentes — an active-duty officer — would take advantage of an early retirement program.

The program, referred to as temporary early retirement authority, had lapsed for Coast Guard officials at the end of the 2018 fiscal year, and, according to people briefed on the discussions, Department of Homeland Security officials began pressing Congress in November to reinstate it. Administration officials said they had been told that Mr. Fuentes discussed the program with officials at the Department of Homeland Security, and after reporters raised questions with lawmakers of both parties, a provision to reinstate it was abruptly pulled from a House bill on Wednesday.

The White House declined to answer questions about whether Mr. Fuentes had pressed to have the program restarted, saying only that he planned to remain on for a time as a senior adviser to aid in the transition to a new chief of staff. But in interviews, nearly a dozen White House and administration aides, none of whom would speak on the record, raised concerns about how they believed Mr. Fuentes planned to use government resources in the coming months.