SIERRA VISTA, Ariz. — Kari Lake has a strategy to get elected in 2022.

Keep talking about 2020.

Minutes into her pitch at the Cochise County Republican headquarters in the suburbs of southern Arizona, Ms. Lake zeroed in on the presidential election 18 months ago, calling it “crooked” and “corrupt.” She claimed nearly a dozen times in a single hour that the 2020 election was stolen from Donald J. Trump, a falsehood that the audience — some of whom wore red hats reading “Trump Won” — was eager to hear. Ms. Lake, a former local Fox News anchor who won Mr. Trump’s endorsement as she campaigns to become Arizona’s next governor, calls the 2020 election a key motivation in her decision to enter the race.

“We need some people with a backbone to stand up for this country — we had our election stolen,” Ms. Lake said in an interview after the Cochise County event in March, adding, “I don’t know if it’s a winning issue, but it’s a winning issue when it comes to saving this country.”

Republicans in many states have grown increasingly tired of the Stop the Steal movement and the push by Mr. Trump to reward election deniers and punish those who accept President Biden’s victory. At a time when Mr. Biden’s approval ratings are sinking, leaders in the party are urging candidates to focus instead on the economy, inflation and other kitchen-table issues.

But 12 weeks before its Republican primary in August, Arizona shows just how firm of a grasp Mr. Trump and his election conspiracy theories still have at every level of the party, from local activists to top statewide candidates. And this week’s victory for J.D. Vance, the “Hillbilly Elegy” author who received the former president’s endorsement in the Republican primary for an Ohio Senate seat, shows that loyalty to Trumpism goes a long way in battleground states.

Still, some establishment Republicans worry that party leaders have gone too far and are effectively handing the closely divided swing state to Democrats in November.

“Anybody who is still re-litigating 2020 will lose the general election,” said Kathy Petsas, a Republican who has served as a precinct captain and collected signatures for several candidates this year. “I think people at home have caught on, and I don’t think a lot of our candidates have caught on.”

Two forces have helped ensure election denialism remains a core issue in Arizona: the Republican-sponsored and widely derided review of the presidential vote in the state’s largest county, and Mr. Trump’s continued attacks on the Republican governor, Doug Ducey, for rebuffing his efforts to block election certification. More than three dozen Republicans running for office in Arizona — including six candidates for statewide posts — have made denying the 2020 results a centerpiece of their campaigns, according to two groups tracking candidates, States United Action and Pro-Democracy Republicans. States United Action is nonpartisan; Maricopa County’s top elections official, a Republican, began Pro-Democracy Republicans earlier this year.

In interviews with more than a dozen voters at Ms. Lake’s campaign events, nearly all said “election integrity” was their top issue, and none believed that Mr. Biden was the legitimate winner of the presidential election.

“We need strong Republicans to get rid of the RINOs who aren’t willing to do anything, like our governor,” said Claribeth Davis, 62, using the acronym for “Republicans in name only” to refer to Mr. Ducey. Ms. Davis, a medical aide, said she recently moved from the Phoenix suburbs to Cochise County’s Sierra Vista, a rural section of southern Arizona, to “be with more like-minded people.”

Numerous courts and reviews have found no evidence of widespread fraud in the 2020 election. The Republican-ordered review by Cyber Ninjas, a now-defunct company with no previous experience in elections, concluded that there had actually been even more votes for Mr. Biden and even fewer for Mr. Trump in Maricopa County. The county’s board of supervisors rebutted nearly all of the group’s claims. But none of that has tamped down the fervent belief among many Republicans that control of the country has been snatched away from them.

“There’s nothing but elitists in charge,” said Suzanne Jenkins, a 75-year-old retiree who described herself as a Tea Party Republican and who drove about an hour to Sierra Vista to hear Ms. Lake speak.

There has been little political upside for moderate and more establishment Republicans in Arizona to speak out against the party’s far-right wing. Instead, the handful of them who have done so have faced protests, censure from local Republican organizations and harassment. Bill Gates, the Republican chairman of the Maricopa County Board of Supervisors, who has repeatedly defended the state’s 2020 election, has received death threats.

“There’s not enough pushback,” said State Senator Paul Boyer, a Republican who is not running for re-election. “Because everyone is afraid of a primary.”

For generations, Arizona was a reliably red state. Even as Senator John McCain fashioned himself into a moderate maverick, the state was a hotbed of conservative anti-immigration politics that helped give rise to Mr. Trump’s candidacy and presidency. Mr. McCain’s name is now invoked as an insult by conservative Republicans, including Ms. Lake.

But in the last four years, voters have elected two Democratic senators and chosen a Democrat for president for the first time in more than two decades, though Republicans remain in control of the State Legislature and the governor’s mansion.

Arizona has long been a source of right-wing enthusiasm for the national party. The former Maricopa County sheriff, Joe Arpaio, made national headlines in the early 2000s for his anti-immigrant policies, and in 2010 the Legislature passed what became known as the “show me your papers” law, effectively legalizing racial profiling. It was later struck down, and Mr. Arpaio is now running for mayor in a Phoenix suburb.

Ms. Lake, who quit her job as an anchor for the local Fox News station because of what she called its bias and dishonesty, frequently blasts the media as “brainwashed,” “immoral” and “the enemy of the people.” And her widespread name recognition has helped give her an early lead in the polls.

But winning the crowded Republican primary is far from certain. Ms. Lake faces especially fierce opposition from Karrin Taylor Robson, a Phoenix-based business owner who has contributed millions to her own campaign. Already, the race to replace Mr. Ducey, who cannot run again because of term limits, has become among the most expensive governor’s races in state history, with $13.6 million in spending so far.

Ms. Taylor Robson has not made the 2020 election the major focus of her campaign, but when asked whether she considered Mr. Biden the fairly elected president, she responded in a statement, “Joe Biden may be the president, but the election definitely wasn’t fair.”

Ms. Lake says Arizona should finish the border wall that Mr. Trump began building. She has emphasized her ties to the former president, appearing with him at his rally in the state earlier this year, fund-raising with him at his Mar-a-Lago club in Florida and including his name on her campaign signs.

Ms. Lake has made conspiracy theories a centerpiece of her campaign — releasing a television ad that told viewers that if they were watching the ad, they were in the middle of a “fake news” program. “You know how to know it’s fake?” she says to the camera. “Because they won’t even cover the biggest story out there: the rigged election of 2020.” She also touts her endorsement from the chief executive of MyPillow, Mike Lindell, a key financier of right-wing efforts to discredit the 2020 election.

From first-time candidates to incumbents in Congress and the State Legislature, many Republicans in Arizona have increasingly embraced an extremist brand of right-wing politics.

Representative Paul Gosar and State Senator Wendy Rogers both spoke at the America First Political Action Conference, a group with strong ties to white nationalists, and both were censured by their legislative bodies for their violent rhetoric and antics. Ms. Rogers and State Representative Mark Finchem, a Republican who is running for secretary of state, have acknowledged ties to the Oath Keepers militia group. Ron Watkins, who is widely believed to have played a major role in writing the anonymous posts that helped spur the pro-Trump conspiracy theory known as QAnon, is running for Congress. Jim Lamon, a Republican running for U.S. Senate, falsely claimed to be an elector for Arizona last year.

Even Mr. Ducey, who was formally censured by the state Republican Party last year for his handling of the coronavirus pandemic, has acknowledged the energy on the state’s hard-right, signing a bill that will require proof of citizenship to vote in federal elections. When reporters asked about his support for Ms. Rogers, Mr. Ducey said that “she’s still better than her opponent,” a Democrat, though he later applauded the Legislature’s vote to censure her. Mark Brnovich, the Arizona attorney general who is now running for U.S. Senate, has faced repeated criticism from other Republicans, including Ms. Lake and Mr. Trump, and accusations that he is dragging out the investigation into the presidential election.

A few Republican candidates have made the economy and immigration the focus of their campaign. But even among those candidates, almost none have offered a full-throated defense of the 2020 election. Some Republicans believe that while focusing on 2020 is both irresponsible and politically unwise, it may not matter in Arizona, where the president’s approval rating is now at its lowest since he took office, a dive largely driven by independent voters.

Because independent and third-party voters make up roughly 34 percent of the electorate, it is impossible to win the state with Republicans alone. Ms. Lake and other candidates like her may have already hit a ceiling even among primary voters, as polls show many voters remain undecided, and there is evidence of growing support for other candidates.

“I am concerned that if these people get elected it will make another decade of craziness,” said Bob Worsley, a former state senator who describes himself as a moderate Republican. “I don’t know who has the stature to say, ‘Let’s bring this party back, bring the establishment base back into power.’ Now we’re a purple state and we don’t have a John McCain to try to crack the whip.”