When Elon Musk and Vivek Ramaswamy, the businessmen that President-elect Donald J. Trump tapped to lead his new Department of Government Efficiency, met with lawmakers in early December, they laid out their plans for cutting federal spending and eliminating waste.

Less than two weeks later, they helped topple a 1,500-page spending bill and brought the federal government to the brink of a shutdown over objections to the billions of dollars of so-called pork spending in the legislation. But the streamlined package that lawmakers ultimately passed failed to offer spending restraint.

During the negotiations, Mr. Trump even called for abolishing the nation’s statutory debt limit, which Republicans have long used as a tool for forcing painful budget cuts.

The frenzy demonstrated the clout that Mr. Musk and Mr. Ramaswamy have as they establish their new waste-cutting enterprise. But the outcome also underscored the limits the initiative will face as it tries to curb spending. In recent decades, the federal government has become increasingly sprawling and Congress has become more fractious, making it difficult to put a dent in a national debt that has topped $36 trillion.

In under a month, Mr. Trump will assume the presidential megaphone with Mr. Musk and Mr. Ramaswamy as his spending enforcers. But budget experts see little hope that the three will be able to meaningfully shift the nation’s fiscal trajectory. The Congressional Budget Office projects that the national debt will reach 166 percent of gross domestic product by 2054, up from about 99 percent of G.D.P. at the end of 2024.