This article is based on interviews with nearly a dozen people familiar with the administration’s knotty relationship with the proposal.

Yucca Mountain, in the desert about 100 miles northwest of Las Vegas, was conceived as a permanent storage place for the nation’s radioactive waste, which is currently scattered across dozens of holding sites around the country.

Nationally, Republicans have long favored the proposal, which was developed in the late 1980s and signed into law by President George W. Bush in 2002. But Nevada politicians of both parties have remained steadfastly opposed to the policy, which is deeply unpopular in the state.

“I don’t know of a major elected official in Nevada today, or in the last five years or 10 years, for that matter, that hasn’t specifically pushed to keep the waste out of the state,” Mr. Heller said.

The project was halted by President Barack Obama, partly at the urging of Harry Reid, a Democrat from Nevada who was the Senate majority leader at the time, but most Republican leaders outside of the state remained supportive. While the plans for Yucca remain law as set under Mr. Bush, Congress has never moved to fund it since.

People close to Mr. Trump, who won the Republican nomination in what amounted to a hostile takeover of the party, say he never favored the idea despite suggesting at the end of the 2016 presidential campaign that he was looking at it. But he also did not care enough to intervene as his previous energy secretary, Rick Perry, supported the measure, and as the Office of Management and Budget listed $120 million in the president’s budget to restart the licensing process of the site. It was listed as one of the administration’s priorities.

Two of Mr. Trump’s political advisers, Bill Stepien and Justin Clark, flagged Yucca Mountain early on as a political danger zone, particularly if Mr. Trump wanted to try to put Nevada in play in 2020.