“It was as if he was dealing with someone else but himself,” Mr. Davis recalled of the meetings, which included himself, Mr. Salter and Carla Eudy, the senator’s longest-serving aide. Cindy McCain, his wife, sometimes called in. When she didn’t, it fell to Mr. Davis to fill her in.

In the spring, Mr. McCain began the uncomfortable task of asking people to speak for him after he died. In April, he approached former Presidents Barack Obama and George W. Bush, a bipartisan request to the men who defeated him in his quests for the White House.

But prominent politicians will not be the only participants. Pallbearers include friends Mr. McCain made over the years, including the actor Warren Beatty and Frederick W. Smith, the founder of FedEx. Larry Fitzgerald, the wide receiver who played for Mr. McCain’s beloved Arizona Cardinals, was asked to speak at Thursday’s memorial service in Phoenix.

Some received messages by phone, and others were asked in person. Former Vice President Joseph R. Biden Jr. was among those summoned to Sedona, when Mr. McCain began executing his funeral plans with a newfound urgency.

They spoke for hours before Mr. McCain asked Mr. Biden to deliver a eulogy at his funeral in Arizona. Mr. Biden immediately accepted, said a person close to the vice president, and he will also serve as a pallbearer on Saturday in Washington. Jim Mattis, Mr. Trump’s secretary of defense, said that he had been asked long ago to be a pallbearer at the final event, a private service that will be held on Sunday at the United States Naval Academy in Annapolis, Md., where Mr. McCain is to be buried.

“I’ve known that for months,” Mr. Mattis said of the senator’s request. “And it’s an honor.”

Vladimir Kara-Murza, a Russian activist who survived two poisoning attempts for his opposition to the government of President Vladimir V. Putin, said that Mr. McCain, who was widely seen as one of the Russian leader’s fiercest detractors, had also asked him in April to be a pallbearer.