David Perdue challenged Gov. Brian Kemp because of Donald Trump’s fury over his 2020 loss. Thoroughly outflanked and failing to gain traction, he is now staring down defeat.In September 2021, former Senator David Perdue was hemming and hawing about running for governor of Georgia. Over dinner with an old friend on Sea Island, he pulled out his iPhone and showed the list of calls he’d gotten from Donald J. Trump, lobbying him to take the plunge.“He said Trump called him all the time,” said Martha Zoller, a former aide to Mr. Perdue who now hosts a talk radio show in Gainesville, Ga. “He showed me on his phone these multiple recent calls and said they were from the president.”Ms. Zoller and a legion of other former Perdue aides and advisers told the former senator that running was a bad idea. He listened to Mr. Trump instead.Now, Mr. Perdue is staring down an epic defeat at the hands of Gov. Brian Kemp, the Republican whom Mr. Trump has blamed for his 2020 loss more than any other person. The Perdue campaign is ending the race low on cash, with no ads on television and a candidate described even by his supporters as lackluster and distracted.“Perdue thought that Trump was a magic wand,” said Newt Gingrich, the former House speaker and a Trump ally, who was among Mr. Perdue’s highest-profile Georgia supporters. “In retrospect, it’s hard to understand David’s campaign, and it’s certainly not the campaign those of us who were for him expected.”Mr. Perdue’s impending downfall in Tuesday’s primary for governor looms as the biggest electoral setback for Mr. Trump since his own defeat in the 2020 election. There is perhaps no contest in which the former president has done more to try to influence the outcome. Mr. Trump recruited, promoted and cleared the field for his ally, while assailing Mr. Kemp, recording television ads and giving $2.64 million to groups helping Mr. Perdue — by far the most he has ever invested in another politician.Yet the race has exposed the limits of Mr. Trump’s sway, especially against entrenched Republican incumbents.Gov. Brian Kemp campaigning with former Gov. Chris Christie of New Jersey in Alpharetta, Ga., this past week. A recent poll showed him leading the Republican primary by more than 30 percentage points.Nicole Craine for The New York TimesMr. Perdue’s failures were not just of his own making. He was outflanked by a savvy incumbent in Mr. Kemp who exploited the powers of his office to cut off Mr. Perdue from allies — including Mr. Perdue’s own cousin Sonny, a former governor and Trump agriculture secretary whom Mr. Kemp’s allies appointed chancellor of the University System of Georgia.Mr. Kemp also appeared to punish those who crossed him: One congressional seat was drawn to exclude the home of a candidate whose father, a Perdue supporter, had publicly criticized the governor.And he offered goodies to voters, including a gas-tax holiday that conveniently runs through the end of May, just past the primary.How Donald J. Trump Still LoomsGrip on G.O.P.: Mr. Trump remains the most powerful figure in the Republican Party. However, there are signs his control is loosening.A Modern-Day Party Boss: Hoarding cash, doling out favors and seeking to crush rivals, Mr. Trump is behaving like the head of a 19th-century political machine.Power Struggle: Led by Senator Mitch McConnell, a band of anti-Trump Republicans is maneuvering to thwart the ex-president.Post-Presidency Profits: Mr. Trump is melding business with politics, capitalizing for personal gain.Just the Beginning: For many Trump supporters who marched on Jan. 6, the day was not a disgraced insurrection but the start of a movement.On Thursday, as Mr. Perdue campaigned outside the Semper Fi Bar and Grille in Woodstock, Ga., he was not conjuring up a path to victory but haggling over the scope of his widely expected defeat, after a Fox News survey showed him down 32 percentage points.“Hell no, I’m not down 30 points,” insisted Mr. Perdue, whose campaign did not respond to requests for comment for this article. “We may not win Tuesday,” he added, “but I guaran-damn-tee-you we are not down 30 points.”The key threshold on Tuesday is 50 percent: Mr. Kemp must win an outright majority in the five-candidate field to avoid a one-on-one runoff in June.The story of Mr. Perdue’s effort is less one of political collapse and more of a failure to launch. From the moment he announced his candidacy in December, Mr. Perdue never demonstrated the same commitment to winning that he displayed in his first Senate race in 2014.His case for ousting Mr. Kemp was always largely based on support from the former president. Mr. Perdue argued at his campaign introduction that the governor had so alienated the party’s Trump faithful that they would not rally around Mr. Kemp against Stacey Abrams, the presumptive Democratic nominee and a leading villain for Republicans.But Mr. Perdue, 72, a wealthy former chief executive of Dollar General, never came close to matching the $3.8 million of his own money he put into his 2014 Senate race. He invested just $500,000 in his bid for governor.That is less than he and his wife spent last year for a waterfront lot on a secluded peninsula on scenic St. Simons Island, a purchase made not long after his runoff defeat at the hands of a then-33-year-old Democrat that delivered Senate control to Democrats. A permit to build a nearly 12,000-square-foot mansion worth an estimated $5 million — on land including “over 625 feet of lake frontage,” according to the listing — was granted two weeks after he declared his candidacy, records show.Mr. Perdue’s home remains under construction on St. Simons Island in Georgia. Parker Stewart for The New York TimesMr. Trump has simultaneously invested heavily in Mr. Perdue, with his $2.64 million, and sought to avoid blame as the candidate has faltered, telling The New York Times in April that the news media’s focus “should be on the endorsements — not the David Perdue one” to measure his influence.Mr. Trump’s last rally in Georgia came in late March. He did not return, as Perdue allies had hoped, instead holding a conference call for supporters in early May.“I am with David all the way because Brian Kemp was the WORST governor in the Country on Election Integrity!” Mr. Trump insisted Friday on his Truth Social messaging platform.Mr. Perdue, like candidates for governor in Idaho and Nebraska this month, learned that a Trump endorsement alone does not assure the support of Trump voters or Trump donors.“The Trump endorsement is very important, but it’s only an endorsement,” said former Representative Jack Kingston, who lost the 2014 Senate primary to Mr. Perdue and is a former Trump adviser. “It’s not an army of infrastructure and door-knockers the way it would be if you have the Sierra Club or the N.R.A. or the A.F.L.-C.I.O.”Mr. Perdue, second from left, with Senator Kelly Loeffler, left, President Donald J. Trump and Melania Trump shortly after the 2020 election. Mr. Perdue and Ms. Loeffler lost to Democrats in early 2021.Doug Mills/The New York TimesThe juxtaposition between the Kemp and Perdue camps was particularly stark on Friday.Mr. Kemp was outside Savannah, announcing that Hyundai was investing $5.5 billion in an electric battery and vehicle manufacturing plant, one of the largest economic development projects in Georgia history. There was a champagne toast.Mr. Perdue was nearby holding an endorsement event with Sarah Palin, the 2008 Republican vice-presidential nominee, who is making her own comeback attempt in a House race in Alaska.“I would rather be standing on the stage announcing 7,500 jobs than standing next to Sarah Palin,” said Mr. Kemp’s lieutenant governor, Geoff Duncan, a fierce Trump critic who opted not to run for re-election this year.Randy Evans, a Perdue supporter who served as ambassador to Luxembourg in the Trump administration, said the Kemp operation had been ruthless in using what he called the “bullying” powers of the governorship.Mr. Evans’s son, Jake, is running for Congress in the Atlanta suburbs. When Kemp-aligned Republican legislators drew new lines in redistricting, the younger Mr. Evans was suddenly drawn out of the district in which he had been planning to run.“They cut a sliver about the size of your little finger,” the elder Mr. Evans said. “Jake had to move, buy a new house.”Mr. Kemp, 58, leveraged the powers of incumbency in other crucial ways. He signed a measure to provide tax refunds of up to $500 for married couples, then announced on May 11, after early voting had begun, that those checks were in the mail. He appealed to rural Georgians by raising pay for teachers, and pleased conservatives by signing sweeping legislation to restrict voting access, expand gun rights and forbid school mask mandates.Mr. Kemp at a campaign stop in Canton, Ga., this past week. He has signed several conservative priorities into law over the past year.Nicole Craine for The New York TimesMr. Perdue’s efforts could seem feeble in comparison. In March, he attacked Mr. Kemp for recruiting an electric truck maker to open a factory in rural Georgia — creating thousands of jobs — because George Soros, the prominent Democratic donor, had recently invested in the company.The Kemp-Perdue contest was steeped in the drama of personal betrayal.Mr. Kemp had spent weeks campaigning with Mr. Perdue before the senator’s defeat in the January 2021 Senate runoff election. By then, Mr. Kemp had infuriated Mr. Trump by defending the legitimacy of Georgia’s presidential results.Last spring, Mr. Kemp’s aides said, Mr. Perdue assured Mr. Kemp that he did not intend to run for governor. That June, Mr. Perdue introduced the governor at the Georgia Republican Party’s annual convention.In 2018, Mr. Perdue and Mr. Kemp appeared together during Mr. Kemp’s campaign for governor.Audra Melton for The New York TimesBut Mr. Kemp, cannily, had already begun the process of installing Sonny Perdue, a popular former governor, to run Georgia’s state universities — an appointment that effectively put him on the sidelines. (Sonny Perdue, through a spokesman, declined to comment.)Mr. Kemp also pre-emptively secured the loyalty and fund-raising might of Alec Poitevint, a South Georgia businessman who had served as campaign chairman for David Perdue’s Senate campaigns and Sonny Perdue’s campaigns for governor — one of many ways the Kemp operation boxed out Mr. Perdue financially.Mr. Poitevint said he was among a host of longtime David Perdue supporters who had urged him not to run.“I didn’t think it was serious,” Mr. Poitevint said. “I expressed the fact that I didn’t agree with it, that I thought that the governor had done a great job and deserved re-election.”Shunned by the state’s political establishment, Mr. Perdue tried framing himself as a political outsider — “I’ve been an outsider since I got into politics,” he said on Thursday — but that is a difficult case to make for a former senator boasting of his support from a former president.Even Mr. Trump’s $2.64 million infusion was swamped by the $5.2 million in television ads paid for by the Republican Governors Association to aid Mr. Kemp.For all of Mr. Trump’s attacks on Mr. Kemp, the governor never struck back. Mr. Kemp’s advisers believe that discipline helped provide permission for even the most devoted Trump supporters to stick with the governor.Mr. Perdue’s campaign, meanwhile, was laser-focused on falsehoods about 2020 — repeating Mr. Trump’s lie and blaming Mr. Kemp for President Biden’s election.Mr. Evans, the former ambassador who in early 2021 had tried to broker a peace deal between Mr. Trump and Mr. Kemp, campaigned for Mr. Perdue but said he saw little effort to define a distinctive platform. “As far as having an existence that existed independent of Trump, I really didn’t see that materialize,” Mr. Evans said.Mr. Kemp’s lieutenant governor, Mr. Duncan, summarized the arc of the Perdue candidacy.“David Perdue made a bad bet six months ago when he jumped in the race and thought, ‘Because Donald Trump likes me, I’m going to win,’” Mr. Duncan said. “He bet wrong.”Maya King More