Would a 3-Way Arizona Senate Race Help Kari Lake? Her Party Isn’t So Sure.

Republicans are growing anxious that their chances of capturing a Senate seat in Arizona would be diminished in a potential three-way race that included Kyrsten Sinema, the independent incumbent.

While Ms. Sinema hasn’t announced whether she will run for re-election, the race already includes Representative Ruben Gallego, a Democrat, and Kari Lake, a Republican scheduled to host her first campaign rally on Tuesday.

Many political strategists had figured that a re-election bid from Ms. Sinema, who dropped her Democratic affiliation last year, would split votes in her former party and increase the odds that Ms. Lake, the controversial front-runner for the Republican nomination, would be sworn in to the Senate. Arizona, along with West Virginia, Montana and Ohio, has been seen as among the best opportunities for Republicans to pick up Senate seats next year and win back a majority.

But private and public polling has suggested that Ms. Sinema is viewed much more favorably by Republican voters than by Democrats. Those surveys indicated that Mr. Gallego would benefit in a three-way race.

“Some of the early conventional wisdom about this race assumed there would be more Democratic defections,” said Austin Stumpf, a Democratic consultant in Arizona. “But party unity among Democrats is hard to overstate. It’s a real phenomenon right now.”

Republicans expressed their concerns as Ms. Lake, a TV-anchor-turned-conservative-firebrand, made an otherwise amicable visit to Washington last week. While she met with a half-dozen Republican senators, many of whom offered campaign assistance or asked to have their photos taken with her, conversations among aides revealed worries about current polling. One Lake adviser described being surprised by the level of “freaking out” by Washington Republicans.

In response, Ms. Lake’s campaign has produced a nine-page internal memo aimed at reassuring the party that she stands to benefit the most from a three-way race. She was also expected to take aim at Ms. Sinema with some of her most withering attacks during her opening campaign event on Tuesday, according to people familiar with the planning, in an attempt to address the concerns that an independent bid by the senator could siphon off a significant share of Republican votes.

The previously unreported memo relies largely on recent turnout trends in Arizona to point to built-in advantages for Republicans.

While Republicans account for roughly 35 percent of registered voters in the state, they typically make up about 40 percent of turnout, according to the memo. Arizona’s unusually large bloc of independent voters accounts for 34 percent of the voter rolls, but makes up a smaller share of turnout, typically between 26 percent and 29 percent, according to the memo.

That means that Ms. Lake — who struggled to unite Republicans during her unsuccessful bid for governor last year as she attacked fellow Republicans, falsely insisted that former President Donald J. Trump had won the 2020 election and later refused to accept her own defeat — should have “significantly more elasticity in shedding Republican voters” than Democrats, according to the memo. (First, Ms. Lake will have to win the Republican primary race; her early rivals include Mark Lamb, a right-wing sheriff and fellow Trump ally.)

The memo also calculates that if Mr. Trump captures another Republican presidential nomination — and wins roughly the same number of votes in Arizona next year as he did in 2020 — then Ms. Sinema’s best path to victory would require more than 600,000 Arizonans to split their ballots between him and the incumbent senator. That total would be about 35 percent of Mr. Trump’s votes.

“This is incredibly unlikely in the Trump era of American politics,” the memo says, noting that split-ticket voting is “near all-time lows.”

One of the private polls that showed Mr. Gallego leading the race, in part because Ms. Lake appeared to be losing Republican votes to Ms. Sinema, was from Chuck Coughlin, a longtime Arizona operative, according to people briefed on the survey. Mr. Coughlin declined to comment on specific findings in his poll, but said that while Ms. Sinema would be a significant underdog if she sought re-election, it would also be foolish to count her out.

“Kyrsten is a monstrously strong campaigner, a very effective fund-raiser and has shown a lot of personal strength to do what she’s done in politics, and I don’t want to underestimate that,” Mr. Coughlin said. “All of that is going to be necessary and a lot more for her to be successful.”

The ambiguity about Ms. Sinema’s plans for re-election has confounded political professionals across three time zones separating Arizona and Washington.

Some of those who anticipate she will retire point to fund-raising numbers showing that Mr. Gallego has consistently out-raised her this year. Ms. Sinema is sitting on a considerable war chest of nearly $11 million, but the Arizona Senate race last year drew more than $230 million in spending from the two major-party candidates and multiple outside groups.

Some of those convinced she will seek a second term pointed to a fund-raiser she hosted this year at the Phoenix Open. The annual golf outing attracts a mix of rowdy partygoers and avid golfers, far from the typical Sinema crowd. “That’s like nails on the chalkboard for Sinema,” said Barrett Marson, a Republican operative in Arizona.

Others were encouraged about her prospects after an internal fund-raising prospectus surfaced last month that signaled she and her team were actively charting a path to a second term, telling donors she could win a competitive three-way race as an independent, which is practically unheard-of in modern American politics.

“Kyrsten promised Arizonans she’d be an independent voice who wouldn’t answer to party bosses and would deliver real, lasting solutions to the challenges Arizonans face,” said Hannah Hurley, an aide to Ms. Sinema. “Instead of engaging in name-calling and stupid political insults, Kyrsten has worked with anyone to make Arizonans’ lives better and then get government out of the way — and that’s exactly what she’s done and will continue to do as Arizona’s senior senator.”

Ms. Sinema’s path relies on an unusual coalition of voters, according to the document, which was first reported by NBC News: winning between 10 percent and 20 percent of Democrats, 25 percent to 35 percent of Republicans and 60 percent to 70 percent of independent voters in the state.

The most difficult benchmark may be the projection among independents. Even Senator John McCain — who was famously popular among independent voters — won just 50 percent of that group in his sixth and final victory in the state in 2016, according to exit polls.

Independents also figure to be a top target for Mr. Gallego, an engaging politician with an inspiring personal story who is running to be the state’s first Latino senator. His campaign projects that Latinos account for about 30 percent of unaffiliated voters in Arizona, and he was ahead of both Ms. Sinema and Ms. Lake in the one public poll that has tested all three candidates this year.

“Ruben is in a good spot and he knows it,” said Mike Noble, an Arizona pollster. He noted that early polls showed that people who had heard of Mr. Gallego generally liked him, while Arizonans tended to have negative views of both Ms. Lake and Ms. Sinema.

Still, Mr. Gallego is running his first statewide campaign since first being elected to the state’s most liberal House district in 2014.

He has collected a handful of endorsements from local officials and public encouragement from Yolanda Bejarano, the chairwoman of the Arizona Democratic Party, but the Democratic Senatorial Campaign Committee and the Senate Majority PAC — which combined to spend nearly $40 million in the Arizona Senate race last year — have both remained silent on the prospect of a three-way race.

Stan Barnes, a Republican consultant and former Arizona state legislator, said a potential three-way race offered a unique opportunity for voters because the top candidates would rely on compelling personalities as they pursued their own silos of voters.

“It is about the most exciting thing I have seen in terms of politics in Arizona in the three decades I have seen,” Mr. Barnes said.