But even Mr. Bolten conceded that nothing mattered if Mr. Priebus could not “develop a good working relationship” with his president. And Mr. Trump, who burned through three campaign managers in less than a year and routinely mocks his aides to their faces, is a hard boss to please, demanding not merely loyalty but, at times, subservience.

The two men got off to a rocky start in 2015. As guardian of his party’s brand, Mr. Priebus called to deliver a stern 40-minute lecture after Mr. Trump railed against Mexican “rapists” at his kickoff rally in early 2015 and objected when Mr. Trump refused to honor a pledge to back the eventual Republican nominee a few months later.

Mr. Trump later fired back, saying that Mr. Priebus “knows better than to lecture me,” adding, “We’re not dealing with a five-star Army general.”

Those encounters were a tutorial for Mr. Priebus, a student of power who believes that proximity to it is the most important step in acquiring it. These days, he is acutely sensitive to Mr. Trump’s moods and has modeled his West Wing role, people close to the R.N.C. chairman say, on the team of no-nonsense general managers who tend to Mr. Trump’s business and resort properties. “He likes people who get things done,” Mr. Priebus said about Mr. Trump recently. “I get things done.”

He has also been careful to avoid direct conflicts with other members of Mr. Trump’s Big Five leadership team, especially the ascendant Mr. Kushner, focusing instead on positioning himself as Mr. Trump’s indispensable organization man.

Each morning, dressed in a crisp dark suit, he prepares for the president-elect a detailed daily agenda and demands reports from staff members on the progress of confirmation prep sessions and communications efforts, a level of rigor that has reassured Mr. Trump his team is ready for the West Wing.

“Reince has done a terrific job,” Mr. Trump said in a statement. “He is always working and will be a great asset to my team in the White House. I hope he will be with me for a long time to come.”

Still, while Mr. Priebus assembled the political machinery that helped secure a Trump win, he has not fully cracked the circle of trust, and the president-elect is not always so glowing about the man he sometimes calls “Reincey.” He often jokes, in an affectionate but tart way, about the R.N.C. chairman’s long-term loyalty, and likes reminding the people around him that Mr. Priebus suggested that he consider dropping out after the release of the “Access Hollywood” tape of Mr. Trump’s crude remarks about women were made public in October.