Republican fears that Sen. John McCain’s battle with cancer could make it harder for the GOP to keep its Senate majority have receded, with a crucial election deadline just days away.

Friends who have visited McCain as he struggles with one of the deadliest forms of brain cancer are encouraged by his recent state, though they recognize the 81-year-old’s condition could deteriorate rapidly.

Republicans in Arizona and Washington are increasingly hopeful McCain will be in office through May 30, the unofficial date for averting a special election for his seat this year. The GOP, which holds a 51-49 majority, is already defending the Arizona seat held by retiring Sen. Jeff Flake (R). Another race in the state would give Democrats a new opening to win control of the Senate.

Under state law, Republican Gov. Doug Ducey would appoint a successor to McCain if the seat is vacant. Ducey is not speculating publicly about who he might appoint, even as Republicans in the state have mentioned his chief of staff and the state treasurer as possibilities. Meanwhile, state election officials are girding for a potential legal tussle over the question of whether an election should occur this year.

Clinical neurologist Philip D. Pulaski describes the effects of the kind of brain tumor that Sen. John McCain (R-Ariz.) has been diagnosed with. (The Washington Post)

“If there was a vacancy today and we made a decision on ‘yes, call a special election’ or ‘no, [don’t] call a special election’ ... there is a 99.9 percent chance that litigation would ensue,” said Eric Spencer, election services director in the office of Arizona Secretary of State Michele Reagan, a Republican.

McCain was diagnosed last summer with a glioblastoma, an aggressive type of brain cancer with a poor prognosis. He has been away from the Senate since December undergoing treatment in his home state.

For months, Republicans have feared the worst. While they still worry about the health and life of a man beloved by many in the party, they are less distressed — though still a bit uneasy — about having to fight to keep his seat in what is shaping up as a difficult election year for President Trump and the GOP.

“Not as worried,” was how one Arizona Republican familiar with discussions in the party summed up the sentiment. Another Republican offered a similar assessment, saying “we have to get through the end of the month.” They spoke on the condition of anonymity to discuss a sensitive topic.

Arizona election law says that when a Senate seat is vacated, it is filled at the next general election. The filing deadline for the November election is May 30 at 5 p.m. Many close observers have interpreted this to mean that if there is no vacancy by that time, a special election would happen in 2020, if triggered. 

But Spencer said the secretary of state’s office is not making any declarations about vacancies that don’t exist now. He said factors like a July write-in deadline and guidance his office has previously issued to local officials about this year’s elections could lead to legal disputes.

If there is a vacancy, Ducey’s appointment will likely be influenced by when it happens.

“I think he has probably got different lists for different circumstances,” said a Republican strategist familiar with the governor’s thinking, meaning some possibilities would be stronger to run in 2018 than 2020.

“His criteria for the job are pretty simple,” said the strategist, who spoke on the condition of anonymity. “Number one, they have got to be able to do the job. Second, you’ve got to be able to keep the job. He is not going to appoint a placeholder. Third, what he wants is somebody who actually will put Arizona first.”

That last part means that it has to be someone who is not a national grandstander, the strategist said.

“The governor has made clear that this kind of speculation is totally inappropriate,” said Ducey spokesman Daniel Scarpinato.

Ducey’s chief of staff, Kirk Adams, and recently appointed state treasurer Eileen Klein are seen by Republicans in the state as two possibilities. They did not comment on Friday.

In early April, a long list of possible interim or long-term successors — including McCain’s wife, Cindy, and former senator Jon Kyl — emerged from private conversations among Republicans.

While Republicans remain nervous about McCain’s health, those who have spent time with him in recent weeks have returned upbeat.

“He’s doing good,” said Sen. Lindsey O. Graham (R-S.C.), one of McCain’s closest friends. Graham spoke by phone with McCain this week and spent time with him earlier this month.

Senate Majority Leader Mitch McConnell (R-Ky.) also visited McCain this month.

“We had a lovely hour together, Cindy and John and I out on the back porch of their house which is ... basically an oasis out in the middle of the desert,” McConnell said in an interview with The Washington Post. “And we reminisced about old times, the battles we fought against each other and the battles we fought together. It was a meaningful experience.”

A person close to McCain said he is “in good spirits as he recovers at home in Arizona. He remains engaged on his work in the Senate, and is proud the Armed Services Committee this week overwhelmingly passed the National Defense Authorization Act, which reflects his priorities as committee chairman.”

McCain’s colleagues named the bill in his honor.

McConnell is keeping a close eye on the race to succeed Flake. It is one of nine races he said in the interview would likely decide control of the Senate. Privately, Republicans have voiced concern about the contest.

The GOP primary is shaping up as a three-way race. McConnell’s preferred candidate is Rep. Martha McSally. Former sheriff Joe Arpaio and former state legislator Kelli Ward are running to her right.

Democrats have recruited a formidable and well-funded candidate, Rep. Kyrsten Sinema. Party leaders have been quiet about the McCain seat, reflecting the sensitivity of broaching the topic.

Senate appointments can be consequential decisions. In 1987, Nebraska Gov. Kay Orr appointed banker and former federal official David Karnes to the Senate following the death of Edward Zorinsky.

But Karnes proved to be a flawed candidate, famously announcing at the Nebraska State Fair that “We need fewer farmers.” The gaffe that helped Democrat Bob Kerrey, a former governor, win the seat.

Correction: An earlier version of this story misspelled the name of former Nebraska senator and governor Bob Kerrey.

Paul Kane contributed to this report.