When the Newt Gingrich-led Republican Revolution swept the G.O.P. into power in the House in 1994 for the first time in 40 years and Republicans also won the Senate, the newly invigorated party set out to revolutionize Washington, shrink the bureaucracy and reduce the federal footprint.

To show they were serious about belt-tightening, lawmakers targeted some of their own office space, proposing to get rid of a nondescript House office annex not far from the Capitol.

“This proposed sale is part of the strategy to downsize the government,” Representative Wayne T. Gilchrist, Republican of Maryland and chairman of the Subcommittee on Buildings and Grounds, said at a hearing in October 1995. “While this building is not large, it represents one of a series of actions undertaken by the legislative branch to reduce its size and scope.”

Three decades later, that building is still controlled by Congress, sitting dark and empty as a monument to how hard it can be to impose significant change on the sprawling federal government. In the hallways of Washington, grand plans like the ones President-elect Donald J. Trump and allies like the billionaire Elon Musk are espousing about abolishing federal agencies and drastically cutting spending have a way of encountering political reality.

“They are fighting with the bureaucracy, and the bureaucracy always wins,” said Ray LaHood, who served as a Republican House member from Illinois during the Gingrich era and later became secretary of transportation under President Barack Obama. “They develop to a fare-thee-well every technique possible to stall, delay and make sure things don’t happen.”