PHOENIX — For more than a year, former President Donald Trump has berated Gov. Doug Ducey of Arizona, savaging him for refusing to overturn the state’s presidential results and vowing to oppose him should he run for the Senate this year.

In early December, though, Mr. Ducey received a far friendlier message from another former Republican president. At a golf tournament luncheon, George W. Bush encouraged him to run against Senator Mark Kelly, a Democrat, suggesting the Republican Party needs more figures like Mr. Ducey to step forward.

“It’s something you have to feel a certain sense of humility about,” the governor said this month of Mr. Bush’s appeal. “You listen respectfully, and that’s what I did.”

Mr. Bush and a band of anti-Trump Republicans led by Senator Mitch McConnell of Kentucky are hoping he does more than listen.

As Mr. Trump works to retain his hold on the Republican Party, elevating a slate of friendly candidates in midterm elections, Mr. McConnell and his allies are quietly, desperately maneuvering to try to thwart him. The loose alliance, which was once thought of as the G.O.P. establishment, for months has been engaged in a high-stakes candidate recruitment campaign, full of phone calls, meetings, polling memos and promises of millions of dollars. It’s all aimed at recapturing the Senate majority, but the election also represents what could be Republicans’ last chance to reverse the spread of Trumpism before it fully consumes their party.

Mr. McConnell for years pushed Mr. Trump’s agenda and only rarely opposed him in public. But the message that he delivers privately now is unsparing, if debatable: Mr. Trump is losing political altitude and need not be feared in a primary, he has told Mr. Ducey in repeated phone calls, as the Senate leader’s lieutenants share polling data they argue proves it.

In conversations with senators and would-be senators, Mr. McConnell is blunt about the damage he believes Mr. Trump has done to the G.O.P., according to those who have spoken to him. Privately, he has declared he won’t let unelectable “goofballs” win Republican primaries.

History doesn’t bode well for such behind-the-scene efforts to challenge Mr. Trump, and Mr. McConnell’s hard sell is so far yielding mixed results. The former president has rallied behind fewer far-right candidates than initially feared by the party’s old guard. Yet a handful of formidable contenders have spurned Mr. McConnell’s entreaties, declining to subject themselves to Mr. Trump’s wrath all for the chance to head to a bitterly divided Washington.

Last week, Gov. Larry Hogan of Maryland announced he would not run for Senate, despite a pressure campaign that involved his wife. Mr. Ducey is expected to make a final decision soon, but he has repeatedly said he has little appetite for a bid.

Mr. Trump, however, has also had setbacks. He’s made a handful of endorsements in contentious races, but his choices have not cleared the Republican field, and one has dropped out.

If Mr. Trump muscles his preferred candidates through primaries and the general election this year, it will leave little doubt of his control of the Republican Party, build momentum for another White House bid and entrench his brand of politics in another generation of Republican leaders.

If he loses in a series of races after an attempt to play kingmaker, however, it would deflate Mr. Trump’s standing, luring other ambitious Republicans into the White House contest and providing a path for the party to move on.

“No one should be afraid of President Trump, period,” said Senator Susan Collins of Maine, who won in 2020 without endorsing the then-president and has worked with Mr. McConnell to try to woo anti-Trump candidates.

While there is some evidence that Mr. Trump’s grip on Republican voters has eased, polls show the former president remains overwhelmingly popular in the party. Among politicians trying to win primaries, no other figure’s support is more ardently sought.

“In my state, he’s still looked at as the leader of the party,” Senator Josh Hawley of Missouri said.

The proxy war isn’t just playing out in Senate races.

Mr. Trump is backing primary opponents to incumbent governors in Georgia and Idaho, encouraged an ally to take on the Alabama governor and helped drive Gov. Charlie Baker of Massachusetts into retirement by supporting a rival. The Republican Governors Association, which Mr. Ducey leads, this week began pushing back, airing a television commercial defending the Georgia governor, Brian Kemp, against his opponent, former Senator David Perdue. It was the first time in the group’s history they’ve financed ads for an incumbent battling a primary.

“Trump has got a lot of chips on the board,” said Bill Haslam, the former Tennessee governor.

Mr. McConnell has been careful in picking his moments to push back against the former president. Last week, he denounced a Republican National Committee resolution orchestrated by Mr. Trump’s allies that censured two House Republican Trump critics.

As the former president heckles the soon-to-be 80-year-old Kentuckian as an “Old Crow,” Mr. McConnell’s response has been to embrace the moniker: Last week, he sent an invitation for a reception in which donors who hand over $5,000 checks can take home bottles of the Kentucky-made Old Crow brand bourbon signed by the senator.

Mr. McConnell has been loath to discuss his recruitment campaign and even less forthcoming about his rivalry with Mr. Trump. In an interview last week, he warded off questions about their conflict, avoiding mentioning Mr. Trump’s name even when it was obvious to whom he was referring.

If Senator Lisa Murkowski of Alaska, who is an outspoken Trump antagonist running for Senate this fall, wins her primary, it will show that “endorsements from some people didn’t determine the outcome,” he said.

Ms. Murkowski appears well-positioned at the moment, with over $4 million on hand while her Trump-backed rival, Kelly Tshibaka, has $630,000.

“He’s made very clear that you’ve been there for Alaska, you’ve been there for the team and I’m going to be there for you,” Ms. Murkowski said of Mr. McConnell’s message to her.

Even more pointedly, Mr. McConnell vowed that if Senator John Thune of South Dakota, the second-ranking Senate Republican, faces the primary that Mr. Trump once promised, Mr. Thune “will crush whoever runs against him.” (The most threatening candidate, Gov. Kristi Noem, has declined.)

The Senate Republican leader has been worried that Mr. Trump will tap candidates too weak to win in the general election, the sort of nominees who cost the party control of the Senate in 2010 and 2012.

“We changed the business model in 2014, and have not had one of these goofballs nominated since,” he told a group of donors on a private conference call last year, according to a recording obtained by The New York Times.

Mr. McConnell has sometimes decided to pick his battles — in Georgia, he acceded to Herschel Walker, a former football star and Trump-backed candidate, after failing to recruit Mr. Perdue to rejoin the Senate. He also came up empty-handed in New Hampshire, where Gov. Chris Sununu passed on a bid after an aggressive campaign that also included lobbying from Mr. Bush.

In Maryland, Mr. Hogan was plainly taken with the all-out push to recruit him, although he declined to take on Senator Chris Van Hollen, a Democrat.

“Elaine Chao was working over my wife,” Mr. Hogan recalled of a lunch, first reported by The Associated Press, between Ms. Chao, the former cabinet secretary and wife of Mr. McConnell, and Maryland’s first lady, Yumi Hogan. “Her argument was, ‘You can really be a voice.’”

Mr. McConnell also dispatched Ms. Collins and Senator Mitt Romney of Utah to lobby Mr. Hogan. That campaign culminated last weekend, when Mr. Romney called Mr. Hogan to vent about the R.N.C.’s censure, tell him Senate Republicans needed anti-Trump reinforcements and argue that Mr. Hogan could have more of a platform in his effort to remake the party as a sitting senator rather than an ex-governor.

“I’m very interested in changing the party and that was the most effective argument,” said Mr. Hogan, who is believed to be considering a bid for the White House.

Mr. Romney lamented Mr. Hogan’s decision and expressed frustration. He claimed most party leaders share their view of the former president, but few will voice it in public.

“I don’t see new people standing up and saying, ‘I’m going to do something here which may be politically unpopular’ — in public at least,” Mr. Romney said.

At Mar-a-Lago, courtship of the former president’s endorsement has been so intense, and his temptation to pick favorites so alluring, that he regrets getting involved in some races too soon, according to three Republican officials who’ve spoken to him.

In Pennsylvania’s open Senate race, Mr. Trump backed Sean Parnell, who withdrew after a bitter custody battle with his estranged wife. And in Alabama, the former president rallied to Representative Mo Brooks to succeed Senator Richard Shelby, who’s retiring. But Mr. Brooks, who attended the rally that preceded the Jan. 6 riot at the Capitol, is struggling to gain traction.

One Republican strategist who has visited with Mr. Trump said the former president was increasingly suspicious of the consultants and donors beseeching him.

“He has become more judicious so not everybody who runs down to Mar-a-Lago for the weekend gets endorsed on Monday,” said Senator Kevin Cramer of North Dakota, another Trump ally.

Mr. Trump has made clear he wants the Senate candidates he backs to oust Mr. McConnell from his leadership perch, and even considered making a pledge to do so a condition of his endorsement. Few have done so to date, a fact Mr. McConnell considers a victory. “Only two of them have taken me on,” he crowed, alluding to Ms. Tshibaka in Alaska, and Eric Greitens, the former Missouri governor running for an open seat.

But Mr. McConnell’s biggest get yet would be Mr. Ducey.

With broad popularity and three statewide victories to his name, the term-limited governor and former ice cream chain executive would be a strong candidate against Mr. Kelly, who has nearly $19 million in the bank — more than double the combined sum of the existing Republican field.

To some of the state’s Republicans, Mr. Ducey could send a critical message in a swing state. “It would say we’re getting tired of this,” said Rusty Bowers, speaker of the Arizona State House, who encouraged Mr. Ducey to stand up to Mr. Trump’s “bully caucus.”

Mr. Ducey also has been lobbied by the G.O.P. strategist Karl Rove, the liaison to Mr. Bush, who sought to reassure the governor that he could win.

Mr. Ducey said he believed that this year’s “primaries are going to determine the future of the party.” However, he sounded much like Mr. Hogan and Mr. Sununu when asked about his enthusiasm for jumping into another campaign.

“This is the job I’ve wanted,” he said.

He noted there was one prominent member of the Trump administration, though, who has been supportive. Former Vice President Mike Pence “encouraged me to stay in the fight,” Mr. Ducey said.