Mourners gathered in Washington, DC on Saturday for the memorial service of Sen. John McCain, who died last weekend at the age of 81.

Even as McCain is honored, attention will also soon turn to the process for replacing him in the Senate, where he spent so much of his career.

The former Navy pilot, Vietnam prisoner of war, and Republican presidential nominee spent 30 years as a senator. Arizona Gov. Doug Ducey, a Republican, is legally required to fill vacancies in Arizona’s US Senate delegation and will therefore appoint McCain’s replacement. Whoever Ducey chooses will stay in office until 2020.

The governor has thus far remained silent on whom he has in mind out of respect for McCain and his family. By Arizona state law, he must tap someone of the same party as McCain — meaning a Republican — and he’s ruled himself out.

In a statement mourning McCain’s death, Ducey said Sen. McCain was “one American who will never be forgotten.” He continued, “His dogged patriotism and passion for country made him an inspiration, and a model, for all of us.”

Ducey’s office said he will not name a replacement until after McCain’s burial.

With Republicans holding a slim 51-49 majority in the US Senate, whispers about who will replace McCain have grown louder.

Ducey will be able to pick a replacement for McCain to serve through 2020

Had McCain left office before May 30, his Senate seat would have been on the ballot in Arizona in November 2018. His junior colleague, Republican Sen. Jeff Flake, has already announced he’s retiring, meaning both of Arizona’s seats would have been up for grabs.

But since it’s after May 30, it will likely be Ducey who picks the replacement. There’s nothing in the state’s constitution that allows for a special election after that date, as Amber Phillips at the Washington Post explains:

Election officials told The Washington Post in the spring that there was the possibility of a legal battle to try to hold a special election in 2018 for McCain’s seat, even if candidates have to file after that May 30 deadline. “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. But that was closer to May. Now a federal election is just months away, and no matter what happens to McCain’s seat in the coming days or weeks or months, it seems very probable it won’t be on the ballot again until 2020.

So Ducey would pick a replacement who would serve at least until 2020, the next general election. And the winner of that election would serve the rest of McCain’s six-year term, which ends after the 2022 election, so in January 2023. The replacement has to be a Republican, like McCain.

Members of the GOP are likely breathing a sigh of relief that both of Arizona’s US Senate spots won’t be in limbo, since the contest to take Flake’s seat is expected to be a contentious one. It’s one of the few opportunities Democrats have to win a Senate seat currently held by Republicans in November, with Democrat Kyrsten Sinema consistently polling in the lead ahead of every one of her Republican competitors.

Who might replace John McCain in the Senate

McCain’s death in office marks the first time in Arizona’s more than 100-year history that a governor would have to fill a Senate seat by appointment. Gov. Ducey has not publicly said whom he might consider to take over McCain’s seat, except to say he won’t appoint himself. Ducey’s office had called conjecture about whom he might pick ahead of McCain’s death “disgraceful.”

That hasn’t stopped the speculation, though. Given that Republicans have only a 51-seat majority after Democrat Doug Jones’s win in Alabama, every vote counts, and the GOP is paying attention.

The Arizona Republic listed a number of names that have been floated as potential appointees to replace McCain. They are:

Cindy McCain, 64, the late senator’s wife. She is a philanthropist and business leader and could represent her husband’s legacy while pursuing her own priorities in Washington, such as her advocacy against human trafficking.

Kirk Adams, 45, Ducey’s chief of staff and a former state lawmaker. He ran unsuccessfully for Congress in 2012.

Barbara Barrett, 67, chair of the Aerospace Corporation and former US ambassador to Finland. She was the first woman Republican to run for governor of Arizona in 1994.

Jon Kyl, 76, who from 1995 to 2013 served alongside McCain in the Senate.

The Arizona Republic also mentions real estate development company president Karrin Taylor, former Rep. John Shadegg, state Treasurer Eileen Klein, and former Rep. Matt Salmon.

One possible contender would have been Republican Rep. Martha McSally, but she is already running for the Senate this year to take Flake’s seat. The other was Dr. Kelli Ward, also running for that seat. McSally defeated Ward in the Arizona Republican primary.

McCain’s replacement probably won’t be very consequential in the short term

McCain was considered a less reliable Republican vote than many of his colleagues, and whoever replaces him is likely to be more solidly aligned with the rest of the GOP. Ducey is more or less a traditional Republican himself, and he will likely choose someone his party’s leaders would approve of.

Heading into November, that could smooth the road for Republican leaders on some issues as they try to navigate the 51-49 Senate to get judicial and Cabinet nominees approved and other legislation passed.

However, on the big-ticket items — namely, Obamacare repeal or welfare reform — McCain’s replacement might not make much difference.

The problem for reviving the health care debate, for example, is that a Democrat now occupies the formerly Republican-held seat in Alabama, and Sens. Susan Collins (R-ME) and Lisa Murkowski (R-AK), who have opposed every repeal plan so far, don’t sound like they want to revisit the issue. Those three alone — plus Sen. Rand Paul (R-KY), who opposed the latest iteration of repeal, known as Graham-Cassidy — form an imposing wall for Republican leaders to overcome no matter who fills McCain’s seat.

So on smaller items and appointments, the new Arizona senator could make things a little easier for GOP leaders. But getting any major legislation through a 51-49 Senate in an election year is still going to be tough.

McCain’s office said he passed away at 4:28 pm on Saturday, surrounded by his wife, Cindy, and his family.