Tudor Dixon, the party’s nominee for governor, has ground to make up in her race against Gov. Gretchen Whitmer. She is hoping the former president can rally their party’s base.CLARKSTON, Mich. — As she runs to lead a narrowly divided swing state, Tudor Dixon is pursuing a hazardous strategy in the Michigan governor’s race: embracing Donald J. Trump, and at times emulating his no-holds-barred political style.She hit the campaign trail recently with the former president’s son Donald Trump Jr. and Kellyanne Conway, the onetime Trump White House adviser — and, in Trumpian fashion, made headlines for mocking her Democratic opponent, Gov. Gretchen Whitmer, over a 2020 kidnapping plot hatched against her by right-wing militia members.In other appearances, Ms. Dixon called for a ban on transgender girls playing in girl’s and women’s sports. And on a recent afternoon at an athletic club in an affluent suburb northwest of Detroit, where a life-size cutout of Mr. Trump stood by the doors, she promoted his so-called America First business policies.“‘America First’ — Michigan First — will bring Michigan back together,” she said.The governor’s race between Ms. Dixon and Ms. Whitmer carries high stakes for abortion rights, schools and the future of elections. It is historic — the first time two women have ever gone head-to-head for the position in the state.The contest also serves as a test of whether Ms. Dixon and other Republican candidates can win their general elections by harnessing the grass-roots energy of Trump supporters that propelled them to the top of crowded and chaotic primaries. That approach — which entails a close association with Mr. Trump’s election denialism and other political baggage — worries some Michigan Republicans who believe Ms. Dixon is failing to win over the kinds of suburban and independent voters who are crucial in tight races.But it might be the only option she has. Early voting began on Thursday, and with time running out, Ms. Dixon is short on cash, well behind in polls, still working to shore up support among her Republican base and being pummeled by Democrats on the television airwaves.“Uphill, on icy roads,” said Dennis Darnoi, a longtime Republican strategist in Michigan, describing her path to victory. “It is a challenge, with a month left, for her to make up the kind of ground that she is going to need.”Ms. Dixon has struggled to compete financially with Gov. Gretchen Whitmer, a Democrat. Emily Elconin for The New York TimesMs. Dixon, who is set to appear alongside Mr. Trump at a rally on Saturday in Macomb County, has appeared unfazed, arguing that her recent fund-raising numbers have been high and that her message will ultimately resonate with voters more than Ms. Whitmer’s.Asked about the challenges ahead for the campaign and Democrats’ large spending numbers, Sara Broadwater, Ms. Dixon’s communications director, took shots at pollsters, saying they failed to predict Mr. Trump’s 2016 victory.The State of the 2022 Midterm ElectionsWith the primaries over, both parties are shifting their focus to the general election on Nov. 8.Sensing a Shift: As November approaches, there are a few signs that the political winds may have begun to blow in a different direction — one that might help Republicans over the final stretch.Focusing on Crime: Across the country, Republicans are attacking Democrats as soft on crime to rally midterm voters. Pennsylvania’s Senate contest offers an especially pointed example of this strategy.Arizona Senate Race: Blake Masters, a Republican, appears to be struggling to win over independent voters, who make up about a third of the state’s electorate.Pennsylvania Governor’s Race: Doug Mastriano, the Trump-backed G.O.P. nominee, is being heavily outspent and trails badly in polling. National Republicans are showing little desire to help him.“As Tudor said the other day in response to a similar question, ‘Isn’t it sad that the Democrats have to spend so much money?’” Ms. Broadwater said. “Gretchen Whitmer remains highly vulnerable as pro-Dixon forces begin to fire back and her campaign gains momentum.”Not all Republicans who closely aligned themselves with Mr. Trump have struggled to pivot from the primary election to the general. In Arizona, the Republican nominee for governor, Kari Lake, has taken a similar approach, and has narrowed her race to a dead heat — but unlike Ms. Dixon, she is not facing an incumbent governor like Ms. Whitmer.Other candidates backed by Mr. Trump, like Blake Masters in Arizona’s Senate race and Doug Mastriano in Pennsylvania’s contest for governor, have fallen behind their Democratic opponents as they have struggled to raise money. Another Republican Senate hopeful, J.D. Vance, is facing a closer-than-expected race in Ohio.Mr. Trump has maintained a keen interest in Michigan. He eked out a victory in the state in 2016 by fewer than 11,000 votes before losing to Joseph R. Biden Jr. in 2020 by more than 154,000 votes.Days before the Republican primary in early August, Mr. Trump endorsed Ms. Dixon, a conservative media personality backed by Michigan’s powerful DeVos family.Ms. Dixon, 45, a breast cancer survivor, worked as a steel industry executive until 2017, when she helped create Lumen Student News, a company that produces conservative TV news and history lessons for middle and high school students.In a December 2021 radio interview, she said she aimed to restore students’ faith in the country and combat what she described as “indoctrination” in schools. After helping found Lumen, Ms. Dixon went on to host a news show, “America’s Voice Live,” on weekday afternoons.Ms. Dixon, a former conservative media personality, is allied with Michigan’s powerful DeVos family. Emily Elconin for The New York TimesA cutout of Mr. Trump was on display at a town-hall event where Ms. Dixon spoke on Thursday in Clarkston, Mich. Emily Elconin for The New York TimesOn the stump, Ms. Dixon says she became a vocal critic of Ms. Whitmer’s coronavirus restrictions as she witnessed their negative impact on Michigan’s economy. The safety measures “took a deeply personal turn,” Ms. Dixon’s website states, after her grandmother died in a Norton Shores nursing home that prohibited visits during the pandemic.Ms. Dixon, who has the delivery of someone comfortable in front of an audience, has generated criticism for spreading unfounded claims about voter fraud in the 2020 election and for some of her stances on L.G.B.T.Q. issues, including calling for “severe criminal penalties for adults who involve children in drag shows.”On her website, she calls for a ban to prevent school employees from talking to children in kindergarten through third grade “about sex and gender theory secretly behind their parents’ backs.” And she has said that abortion should be allowed only if it is necessary to save the life of a mother, not in cases of rape or incest.Ms. Dixon’s stance on abortion in particular — in a state where voters tend to favor abortion rights and in November will weigh a ballot measure to enshrine the right to abortion in the state Constitution — is a big reason that some Republicans are worried about her chances. They also fear that underperformance at the top of the ballot could cause the G.O.P. to lose control of the State Legislature.Michigan’s Republican Party has been in a state of turmoil for months.The party’s primary was defined by fierce infighting between its establishment and Trump factions. Its two front-runners for governor were disqualified for turning in petitions with thousands of forged signatures. Another candidate was charged with four misdemeanors related to the Capitol riot.Ms. Dixon managed to rally her fractious party behind her in the race’s final weeks. But even after winning the primary, she remained a relatively little-known political outsider. It did not help that at the G.O.P. state convention later in August, Republicans officially endorsed two preachers of 2020 election falsehoods for top state offices: Matthew DePerno for attorney general and Kristina Karamo for secretary of state.The bruising battles, as well as the lack of financial networks and campaign experience among leading Republican candidates, have made for what Richard Czuba, an independent pollster in Lansing, Mich., called “the worst ticket I have seen from any party in the last 40 years.”“It is great to run as an outsider, especially when you run against an incumbent,” Mr. Czuba said. “But there are two sides of that outsider coin. On the one hand, you can run as the outsider against the establishment. On the flip side, you don’t know how to do this — and that is what is showing.”Ms. Dixon and her running mate, former State Representative Shane Hernandez, after officially securing their nomination at the Republican convention in late August.Emily Elconin for The New York TimesAs the general election began, Democrats rushed to define Ms. Dixon before she had a chance to define herself. As Ms. Whitmer had kept $14 million in her war chest by late August, after accounting for debts and expenditures, Ms. Dixon’s end balance was $523,000, according to the state’s latest available campaign finance reports. Democratic groups have poured more than $41 million into television ads since the August primary, according to the firm AdImpact, which analyzes campaign ad spending. Republican groups, by contrast, have invested about $5.5 million.State party leaders and national Republicans this week pushed back against any notion that the race was out of reach and that Ms. Dixon had been left to fend for herself. This past week, the Michigan Republican Party began its largest ad push against Ms. Whitmer, seeking to paint her as “soft on crime.” Chris Gustafson, a spokesman for the Republican Governors Association, said it might also jump in with more ads soon.“In Michigan historically, we have seen candidates in big races be down in the polls only to come back to win,” Mr. Gustafson said. “We feel Tudor is a strong candidate with a good message. She is within striking distance.”At Ms. Dixon’s event at the athletic club in Oakland County, a panel including former Trump administration officials sat against the tall glass walls of a serene, sunlit indoor pool, as they blasted Mr. Biden’s economic policies and painted a harrowing picture of crime-filled American cities and unchecked immigration at the southwestern border.In a short speech, Ms. Dixon slammed what she characterized as a “radical sex and gender theory” permeating schools and denounced Ms. Whitmer for providing tax incentives to bring a Chinese company to Michigan, rather than an American one.But mostly, she displayed a rare dose of moderation, critiquing Mr. Whitmer’s pandemic restrictions and economic policies, rising crime in the state’s cities, and schools that Ms. Dixon argued had failed to adequately teach students to read and write. They were the kinds of remarks that some establishment and moderate Republicans might be hoping for — and they also seemed to appease the people in the room.Susan Savich, 64, and her 24-year-old son, Jonathan, asked to take photos with Ms. Dixon on her way out. They were opposed to schools teaching children anything but basic skills and traditional beliefs, they said, and Mr. Savich liked that Ms. Dixon was “education first.”They were also relieved to hear that Mr. Trump was coming to the state. “Ms. Dixon is going up against a lot,” Mr. Savich said. More