He responded by texting, calling and buttonholing Republicans, especially Mr. Ryan — badgering him for weeks to bring some version of the bill to the floor and demanding votes despite being short of support, with an angry insistence that tested their two-Cheeseheads-are-better-than-one friendship.
Mr. Priebus’s push for a quick vote chafed some members of the White House staff. Several people on Mr. Trump’s team who were trying to lower expectations were annoyed to find out that Mr. Priebus was openly talking about forcing a vote this week. At times, Mr. Trump himself seemed a little puzzled by his aide’s vehemence, telling legislators, including Mr. Ryan, that while he wanted a win, he did not necessarily need a vote immediately.
And it was Mr. Ryan, not the president, who offered his friend a shout-out at Thursday’s spike-the-football celebration for a bill passed by one chamber of Congress. “I especially want to thank Reince Priebus,” he said as Mr. Trump looked on.
The House’s passage of the health bill was less a victory for Mr. Priebus than a reprieve. It bought him time for a badly needed reset after three chaotic months in a job that has often seemed to overwhelm him — and possibly would anybody else in his position.
“At first, I think Reince wanted to be the gatekeeper, the guy who has control of who comes in and out all day. But you can’t do that with Donald Trump — he won’t let you,” said Senator Lindsey Graham of South Carolina, an on-and-off Republican critic of Mr. Trump who speaks with Mr. Priebus often. “I think he’s learned to play a different role by necessity. He has to stick with organizing things. He has to be the connective tissue. I think he gets that.”
Even with a win, Mr. Priebus remains, at best, the third most powerful player in a top-heavy White House dominated by bigger personalities, a would-be gatekeeper desperately in search of a gate.
“It’s been the most dysfunctional White House in memory, and a lot of it is on Reince,” said Chris Whipple, a documentary filmmaker and author of “The Gatekeepers,” a new book chronicling White House chiefs of staff back to the Truman administration.
“Priebus has made rookie mistake after rookie mistake, and he started by making the biggest one of all: not insisting he be the first among equals,” Mr. Whipple said. “Fatal mistake. I’m not sure anybody could make that demand, but he didn’t even really try.”
“At some point, the president is either going to embrace failure or pick a grown-up, like a C.E.O. or maybe Mattis, as his chief,” he added, referring to Defense Secretary Jim Mattis.
The signature image of Mr. Trump’s first 100 days in office, people close to the president said, is that of Mr. Priebus standing just inside the open door of the Oval Office, agitated and rolling his eyes, as Mr. Trump beckons another seemingly random gaggle of aides, friends, family, visitors, reporters — even the White House decorator — in for an unstructured chat or, worst of all, policy discussions.
Mr. Priebus, who has said he has self-diagnosed obsessive-compulsive disorder, tried at first to restrict these interactions, often by keeping the president busy with ceremonial events like executive order signings and meetings with business leaders.
Over time, Mr. Trump bridled and demanded the unstructured time he had so valued as an executive at Trump Tower. Mr. Priebus, who initially outsourced the details of Oval Office scheduling and paper flow to a deputy, has now taken over those tasks himself. He has reduced the pace of public events and, like a Montessori teacher, modulates structured work time with the slack periods Mr. Trump craves.
In recent days, Mr. Priebus cut back on his stalking-butler tendency to hover over the president, realizing his antsy boss had grown resentful of his constant companionship. “What are you doing in here? Don’t you have health care to take care of?” Mr. Trump asked Mr. Priebus at one recent meeting around his desk, according to a senior White House official.
Mr. Priebus is increasingly focused on big-picture issues like improving the “interagency” process linking the West Wing to the federal bureaucracy. He has also tried to reduce what he calls inputs — the number of people talking to the president each day — to 20 or so from about 50, and to keep Mr. Trump to a tighter schedule through short, agenda-driven meetings: a suggestion made by many outside advisers he consulted, including John H. Sununu, the chief of staff to President George Bush.
That entails trying to cut the number of Oval Office meeting attendees from 15 to eight or fewer, according to an aide.
One small but significant recent victory: excluding Omarosa Manigault, the former “Apprentice” contestant and Trump favorite, from as many meetings as possible.
“The trains are now running on time,” said Thomas Barrack Jr., a close friend of Mr. Trump’s, reflecting a prevailing sense even among Mr. Priebus’s critics in the White House that the situation has improved.
That does not mean Mr. Priebus is entirely running things. He is often elbowed out by a half-dozen other West Wing players — chief among them Mr. Trump’s son-in-law, Jared Kushner, who enjoys many of the powers exercised by a chief of staff (he has told friends he is “a first among equals”), including a virtual veto over some hiring decisions. Mr. Priebus has half-joked that Mr. Kushner has “all the fun” but few of the responsibilities that burden him, according to one longtime Priebus confidant.
“Reince is fundamentally a nice Midwestern guy who is very concerned about not losing friends and not making enemies,” said Charlie Sykes, a veteran Republican operative and radio host in Wisconsin who has been friends with Mr. Priebus for two decades. “He is, at bottom, a pleaser. But he doesn’t want to fail.”
“One of the things that’s made him successful up until now is that he knows how to maintain friendships; he knows how to keep in touch with donors and key players,” Mr. Sykes said. “But I don’t know that he would be the one to crack the whip. At a certain point, you have to be willing to be confrontational and to lose friends. I think that’s very difficult for Reince.”
For all the talk of Mr. Priebus as a potentially moderating force, he has fed some of the president’s most self-destructive impulses, including reviewing a way to sue the news media and vigorously supporting Mr. Trump’s hunt for an order supposedly obtained by the Obama administration to allow the surveillance of Trump campaign officials.
But all of these stresses are worth it, Mr. Priebus has told friends.
One of the party’s most formidable fund-raisers, Mr. Priebus, who declined to be interviewed for this article, is accustomed to swallowing his pride to court richer, more powerful men. So he has a high pain threshold for a boss who still views him, in moments of candor, as a leader of the Republican political establishment that once tried to destroy Mr. Trump.
Mr. Priebus — whose allies say he has always been animated by proximity to power — is nothing if not resilient, however, and he is intent on forging alliances with anyone who can improve his internal standing. In recent weeks, he has tried to capitalize on the growing rift between Mr. Kushner and the White House chief strategist, Stephen K. Bannon.
At the height of the Kushner-Bannon spat last month, Mr. Trump instructed both men to “stop it” or face the boot, and delegated to Mr. Priebus the role of evenhanded mediator. Instead, Mr. Priebus interpreted that as a license to forge an alliance with Mr. Kushner, though the first son-in-law has felt free to use his veto power over the chief of staff, including siding with others to keep Mr. Priebus from promoting his preferred choices for his deputy, according to four West Wing aides.
Mr. Priebus has been reluctant to confront Mr. Bannon directly. But he has quietly sought to undermine Mr. Bannon’s agenda and temper his nativist impulses, and has happily assumed the role of establishment soother. At a dinner last week at the Hay-Adams Hotel with a number of prominent Republicans, including former Vice President Dick Cheney, Mr. Priebus assured the attendees that the North American Free Trade Agreement would not be undone the next day, as Mr. Bannon had sought to do, according to three people with knowledge of the interaction.
He has also bonded with Mr. Kushner and his wife, the president’s daughter Ivanka, over what they all see as Mr. Bannon’s hidden war against them in the news media, especially through Breitbart, the site Mr. Bannon used to run. Mr. Kushner was especially incensed by Breitbart’s speculation that Mr. Priebus would soon be replaced by his ally Gary D. Cohn, the National Economic Council chairman, two people close to him said.
Mr. Priebus is wounded by the speculation and is intensely protective of his image, forged over seven successful years at the Republican National Committee, of competence and effectiveness, even as some of his own colleagues question it.
He has spent so much time in the Oval Office that his own suite in the southwest corner of the White House remains much as his predecessor, Denis McDonough, left it, complete with its vintage World War II and Vietnam-era photographs of naval battles. His own desk is sparsely decorated and often covered with neatly arrayed note cards on which he has written, in fastidious red Sharpie, his daily to-do list or his talking points.
The wall opposite his standing desk features a triptych of flat-screen TVs tuned to basic cable, and he spends much of his day monitoring the chatter, especially the utterances of his fellow Republicans.
When Gov. Chris Christie of New Jersey, a Trump ally and the source of speculation as a future chief of staff, visited the White House recently, Mr. Priebus pulled him into the Roosevelt Room to complain about Mr. Christie’s less-than-helpful comments on TV.
“He’ll text you all the time,” Mr. Graham said. “It will be like, ‘Thanks,’ or ‘Why the hell did you say that?’”