Arizona’s Republican governor is navigating a political minefield as he weighs whom to appoint to the late Sen. John McCain's seat.

Required by state law to name a replacement to fill the seat until the 2020 election, Gov. Doug Ducey will have to balance the demands of state conservatives – some of whom have soured toward McCain’s criticisms of President Trump and his immigration stance – with the desire to respect the legendary GOP senator's legacy and family by appointing a successor in his image.

And he has to do this while the state is in the middle of a heated midterm race to fill the seat being vacated by Republican Sen. Jeff Flake. Primaries for both parties are being held Tuesday.

“Ducey’s job is both simple and complex at the same time,” Jason Rose, a political consultant and founder of Rose + Moser + Allyn Public Relations in Scottsdale, told Fox News. “It needs to be someone who can step into McCain’s very big shoes, and that won’t be easy.”

While talk of McCain’s replacement has been churning since he was diagnosed with brain cancer more than a year ago, Ducey has refused to discuss possible successors out of respect for McCain and his family. Ducey’s office also noted on Sunday that he will make no announcement of a replacement until after McCain’s burial at his alma mater, the U.S. Naval Academy, later this week.

“Out of respect for the life and legacy of Senator John McCain and his family, Governor Ducey will not be making any announcements about an appointment until after the Senator is laid to rest,” Daniel Ruiz II, a senior adviser to Ducey, told PBS. “Now is a time for remembering and honoring a consequential life well lived.”

Ducey’s silence on the matter, however, has not stopped analysts from weighing in on who could make the shortlist to replace McCain in the Senate, with everyone from former U.S. Senate Republican whip Jon Kyl to former Rep. Matt Salmon to former ambassador to Finland Barbara Barrett to McCain’s widow, Cindy, being floated.

Other names being mentioned: Maj. Gen. Michael McGuire, who heads the Arizona Department of Emergency and Military Affairs and is the adjutant general of the state's Army and Air National Guards; Karrin Taylor Robson, whom Ducey appointed to the state Board of Regents in 2017; and Kirk Adams, the former state House speaker who now serves as Ducey's chief of staff.

Some analysts say the choice by Ducey boils down to whether he wants to appoint someone for the long-term or a caretaker who would step aside during the next general election in 2020, in case Ducey himself decides to run for the seat.

"Do I appoint a caretaker or do I appoint someone who will stand for election?" asked Doug Cole, a former McCain staffer and veteran Arizona strategist. "Does he choose from the family?"

Some observers predict the governor will be solicitous to the McCain family's wishes. That's led to widespread speculation that Cindy McCain could be selected, likely under the assumption that she would not run for the seat in 2020. But Cindy McCain's politics are largely unknown.

Despite his role shepherding the nomination of Brett Kavanaugh into the Supreme Court and Republican reticence to upend that process, another caretaker option would be Kyl, now a Washington lobbyist viewed as a safe, uncontroversial choice.

“McCain was an exception to the rule is so many ways,” Rose said. “You can’t really fill his shoes so you have to get someone as close to him as possible. And that would be Jon Kyl. You can’t go wrong with Kyl.”

Arizona operatives speculate that one of two former congressmen from the state, John Shadegg and Matt Salmon, also have a chance to fill the seat. They're both GOP stalwarts who don't have a history of feuding with the base. State Treasurer Eileen Klein could also be a strong candidate in 2020 if Ducey wants to pick someone who'd run for election rather than a caretaker, according to Republican operatives.

“If Ducey decides to appoint a moderate senator, that could help him in the long-term,” Rose said, adding that the governor faces a weak primary challenge from his right in the state's primary elections Tuesday.

The person who previously was seen as McCain's most likely successor is Arizona Rep. Martha McSally. Like the late senator, she's a former fighter pilot — one of the first women to fly in combat and an air force colonel. But she is running for the Senate seat vacated by Flake, who, like McCain, riled the state's conservative base by bucking Trump on immigration and other issues.

Like Ducey, McSally faces a primary on Tuesday, but her challenge from the right has been stiffer than the governor's. It's also illustrated how fraught the McCain issue is for Arizona Republicans.

One of her rivals, former state senator Kelli Ward, ran against McCain in the 2016 GOP primary. On Saturday, hours before McCain died, Ward speculated on Facebook that the McCain family announced the senator was ending medical treatment on Friday to distract from her final push in the primary.

Earlier this month, McSally even avoided mentioning McCain's name while boasting that she'd been with Trump at the signing of the defense bill named in McCain's honor. McCain supporters and the senator's daughter Meghan lacerated McSally for following the president's lead in not mentioning McCain.

Whomever gets the nod from Ducey will be in office until the next general election in November 2020. The interim senator would not be obligated to run in that election. The candidate who is then elected to the Senate seat in November 2020 would complete McCain's term, which expires in January 2023.

If Ducey chooses one of the state’s current congressional members to fill the seat, then a special election would need to be held to fill that empty spot. According to the Arizona State Legislature, that election would have to be held “not less than 120 nor more than 133 days” after the vacancy occurs.

The Associated Press contributed to this report.