Rep. Martha McSally (R-Ariz.) ran for Senate in November and lost to Democratic Rep. Kyrsten Sinema. (Matt York/AP)

Arizona Gov. Doug Ducey has lost enthusiasm for appointing Rep. Martha McSally, a fellow Republican, to the Senate in recent weeks even as Republican leaders in Washington have championed her.

Ducey has made no firm decision and McSally, who narrowly lost this year’s Senate race, remains a finalist to fill the seat that John McCain held for decades, a seat that may soon open up. But her stock has fallen in the eyes of the governor, according to two people familiar with his thinking, as Ducey approaches one of the most significant decisions of his political career.

Ducey’s choice would affect not only the future of the Senate but the 2020 elections in an increasingly competitive battleground state. It could also impact his relationship with Senate Majority Leader Mitch McConnell (R-Ky.), a McSally advocate, as well as other party leaders who want to see more Republican women in Congress.

There are several reasons McSally’s chances have faded, according to the people who spoke on the condition of anonymity to freely discuss private conversations. One is a post-election memo her campaign strategists provided to The Washington Post last month, which attributed her defeat in November to external factors. Among them: strong Democratic fundraising, a geographic disadvantage and voter hostility toward President Trump.

The memo sparked outrage inside Ducey’s circle and among broader swaths of influential Republicans, who felt her team did not own up to its strategic mistakes and was trying to deflect blame for her loss to Democratic Rep. Kyrsten Sinema.

There are also concerns about McSally’s standing among Republican donors.

“There is momentum building for an anybody-but-McSally appointment among the Arizona donor community,” said Dan Eberhart, an Arizona-based oil industry executive and donor to McSally’s campaign this year.

McSally declined to comment for this story.

After McCain’s death in August, Ducey appointed Jon Kyl, a well-known former Republican senator, to fill his seat. Kyl committed to serving through at least the end of this year — making no promises about returning for the 2019 Congress.

Ducey and his closest confidants are preparing for the strong possibility that Kyl will soon announce his departure. Kyl has not said what he plans to do.

One factor working in McSally’s favor is the lack of obvious alternatives who could quickly begin campaigning for a special election in 2020. Another Republican under serious consideration is Kirk Adams, Ducey’s outgoing chief of staff. Adams has never run for statewide office. His last day on the job will be Friday.

Ducey believes the 2020 election could be more challenging for Republicans than it was in 2018, the people who are familiar with his thinking said, and he wants to ensure that whoever he appoints will be well-positioned to hit the ground running and wage a competitive campaign to retain the seat.

The governor and his closest allies are not yet convinced McSally is that person. A Ducey spokesman did not immediately respond to a request for comment.

In a telephone conversation days after the Nov. 6 election, McConnell advised Ducey to consider appointing McSally if there is a vacancy, praising her and arguing that she had a lot of support in the party. In the chat, previously reported by The Washington Post, Ducey listened but made no commitments.

Ducey and McSally met Dec. 3. The people familiar with the governor’s thinking and a third person familiar with the conversation described the meeting as productive. The third person also spoke on the condition of anonymity to describe a private discussion.

Sinema defeated McSally by about two percentage points in November. The Democrat will succeed Republican Sen. Jeff Flake, a vocal Trump critic who is retiring. Her win stood out as a substantial achievement for Democrats in a year when Republicans expanded their Senate majority to 53 to 47.

Ducey won reelection by about 14 percentage points, leading his allies to wonder why McSally lagged so far behind him. The memo provided by McSally’s campaign strategists mentions the governor.

“While true that Ducey outperformed McSally, Governor Ducey was an incumbent with two successful statewide races under his belt. Ducey’s opponent ran as a progressive and the opponent was essentially abandoned by national Democrats,” the memo says.

The memo was written by about 10 people, according to one person close to McSally. The group included campaign consultants Jeff Roe and Travis Smith.

But other Republicans have pointed to McSally’s reinvention as a staunch Trump ally after previously criticizing the president and her decision to distance herself from McCain as factors in her defeat.

Republicans have also complained McSally did not aggressively seize on opposition research about Sinema’s past to brand her as an extremist. Sinema is a former Green Party activist who campaigned as a centrist Democrat this year.

Democrats see an opportunity to expand their gains in Arizona in the coming years. Following the special election for McCain’s seat in 2020, there will be another election for the seat in 2022.

There are at least several potential Democratic candidates, including Mark Kelly, a former astronaut and husband of former congresswoman Gabrielle Giffords; Rep. Ruben Gallego; and Grant Woods, a former chief of staff to McCain who served as state attorney general.

Trump won Arizona by about four percentage points in 2016. Some members of both major political parties have expressed a belief that 2020 could be a more competitive contest.