WASHINGTON — The Republican health care overhaul might never become law, but it has already changed the life of one American: Reince Priebus, who knew it was his best and perhaps last hope of becoming an empowered White House chief of staff.

President Trump placed much of the blame for his first, failed push to repeal the Affordable Care Act in March on Mr. Priebus, the harried and ambitious former Republican National Committee chairman. He told aides that he believed the damaging loss had resulted in no small part from Mr. Priebus’s too-rosy vote-count predictions and his too-cozy relationship with Speaker Paul D. Ryan, a fellow Wisconsinite.

After that defeat, Mr. Trump’s staff noticed that the president had adopted a practice of merging the two men’s names into one long “Ryan-ce,” according to several West Wing aides.

It is unlikely that Mr. Priebus — roundly regarded as a steady party leader but one of the least powerful White House chiefs of staff ever — would have been fired had the second repeal-and-replace plan not passed the House on Thursday. But he viewed it as a personal make-or-break moment, and interviews with two dozen West Wing aides and Republican officials confirmed that another big loss on health care would probably have been an unrecoverable blow to an already weakened Mr. Priebus.