With a promise to expand Medicaid and a focus on turning out Black voters, Brandon Presley is confident he can do what no Democrat has done in 20 years. After stopping by a meet-and-greet in Ridgeland, a porch festival in Vicksburg, the Great Delta Bear Affair in Rolling Fork and an event on a baseball diamond in Yazoo City, Brandon Presley entered a packed room in McComb, launching into the message he believes can get a Democrat — namely, himself — elected governor of Mississippi. He would immediately move to expand Medicaid, which would help resuscitate rural hospitals and provide largely free government health insurance to most low-income adults. He would slash a hated tax on groceries. Above all, he assured the crowd, he would be a very different governor than Tate Reeves, the Republican incumbent, whom he denounced as ensconced in privilege and dented by scandal.“The fight in politics in Mississippi is not right versus left,” Mr. Presley, an elected public utilities commissioner and a former mayor of Nettleton, his tiny hometown in northern Mississippi, said in McComb. “And sometimes, it’s not even Democrat versus Republican. It’s those of us on the outside versus those of them on the inside.” Mr. Presley’s campaign has been a built on a bet that his human touch and populist platform can forge a coalition of Black and liberal-to-centrist white voters, some disaffected Republicans among them, that is robust enough for him to win. It is a test of a blueprint that Democrats have long relied on, but to diminishing effect in recent decades, as Republicans have tightened their grip on power in Mississippi and most of the South.Mr. Presley, left, and Tate Reeves, the Republican incumbent, during a debate on Wednesday.Brett Kenyon/WAPT, via Associated PressYet Mr. Presley has gained decent momentum — and with it, the attention of Democrats outside Mississippi. He has raised more than $11 million since January, far outpacing Mr. Reeves, and has used the money to flood television and radio stations with campaign advertisements. The nonpartisan Cook Political Report recently found that the election had “morphed into a competitive fight.” But it also classified the race as “likely to lean Republican” — a splash of cold water underscoring that, no matter how much ground Mr. Presley gains or optimism he has inspired in Southern Democrats, he still faces difficult odds in a state that has not elected a Democratic governor in 24 years.In the race for governor four years ago, Jim Hood, then the state attorney general and the last Democrat elected to statewide office, was seen as the most viable candidate the party had fielded in Mississippi in more than a decade. Yet he lost to Mr. Reeves by about five percentage points.Still, Mr. Presley sensed an opening. He believed that Mr. Reeves’s shaky popularity ratings, fury over a sprawling scandal involving welfare funds being directed to the pet projects of wealthy and connected Republicans, and dissatisfaction over the state’s eternal struggle for prosperity could allow him to accomplish what previous Democratic candidates could not. If neither candidate wins a majority of the popular vote on Tuesday, the race will go to a runoff on Nov. 28. Mr. Presley has invested enormous effort in mobilizing Black voters, a crucial bloc in a state where nearly 40 percent of the population is Black. But turning out the rest of the coalition that Mr. Presley needs — for example, white working-class voters who might have voted for Mr. Reeves last time — will be instrumental.“You can’t win if you don’t win white crossover votes,” said Byron D’Andra Orey, a political science professor at Jackson State University. For months, Mr. Presley has had marathon days ping-ponging across Mississippi, stopping in all 82 counties. He has become a frequent presence at football games on historically Black college campuses, as well as at festivals and small gatherings in community centers. In each place, he has made the same case: He is not a liberal — he opposes abortion rights — and he is certainly no elite. True, Elvis Presley was his second cousin, but a distant relative’s fame did nothing to boost his family’s fortunes. His mother was left to raise him and his siblings on her own after his father was killed when he was 8. Mr. Presley has become a frequent presence at football games on historically Black college campuses, as well as at festivals and small gatherings in community centers.Emily Kask for The New York Times“I’m white, and I’m country — it ain’t nothing I can do about it,” Mr. Presley told a mostly Black audience at one campaign stop. “But I get up every day and go to bed every night trying to pull Mississippi together.”The state fractures along racial and regional lines, creating a landscape that is anything but homogeneous, even as it tilts heavily in the Republican Party’s favor. The western flank, including the flat expanse of farmland in the Delta, votes for Democrats. Mr. Presley has wagered that one of his goals in particular can unify Democrats and Republicans, Black and many white voters: joining the 40 other states that have expanded Medicaid under the Affordable Care Act. Researchers have forecast that doing so would make the coverage available to roughly 230,000 lower-income adults over six years. Polls in Mississippi — where death rates are among the nation’s highest for heart disease, stroke, diabetes and cancer — have indicated overwhelming support.Mr. Reeves has been adamant in his opposition to expanding Medicaid, pointing to the cost (most of which would be a federal responsibility) and dismissing it as “welfare.” In September, he proposed an alternative that, if approved by federal officials, would increase funding for some hospitals but would not provide coverage for the uninsured. Mr. Presley with a supporter in Fulton, Miss.Houston Cofield for The New York TimesGrant Dowdy, a dentist in Greenville who came to the festival in Rolling Fork, said he was prepared to break a consistent streak of voting for Republicans precisely because of Mr. Presley’s support for Medicaid expansion. Mississippi, he said, “needs to be like every other sensible state in the nation.”But in such a polarized political climate, where party allegiance often outweighs all else, recruiting enough Republicans to tip the scale toward Mr. Presley may prove impossible. In 2001, he became the youngest mayor in Mississippi when was elected to lead Nettleton, a city of some 1,900 people in the state’s northeast. Since then, Mr. Presley, 46, has been elected four times to represent a vast swath of northern Mississippi on the state’s Public Service Commission, which regulates telecommunications, electric, gas, water and sewer utilities. Colleagues and supporters said the position — in a district filled with heavily conservative areas — helped him hone the solicitous approach he is bringing to the governor’s race. Mr. Reeves has cast Mr. Presley as a liberal aligned with President Biden, and his campaign as orchestrated by the national Democratic Party. He has pointed out that most of Mr. Presley’s fund-raising haul has come from outside Mississippi. “Ask yourself: Why are they dropping historic money on Mississippi to flip it blue?” Mr. Reeves said on social media in October. “It’s because they know Brandon Presley will govern like a liberal Democrat.”Mr. Reeves is also emphasizing his conservative bona fides, including tax cuts he has signed and a promise to keep pursuing his ambition of eliminating the state income tax. Mr. Presley has been elected four times to represent a swath of northern Mississippi on the state’s Public Services Commission.Houston Cofield for The New York TimesHe has touted the state’s unemployment rate, which has fallen to just over 3 percent — the lowest it has been in decades. He has also campaigned on raises he approved last year for public schoolteachers that were among the largest in state history, amounting to average increase of about $5,100 a year. Mr. Reeves has also said that his administration is trying to claw back money misspent in the welfare scandal, in which more than $77 million was siphoned from the state’s poorest residents to fund projects like one championed by Brett Favre, the former N.F.L. player, to build a volleyball stadium at the University of Southern Mississippi. Mr. Reeves was the state’s lieutenant governor at the time. Mr. Presley knows how to rouse a crowd, evoking a pastor in one moment and insult comic the next. He skewered Mr. Reeves at the candidate forum in McComb to cheers of approval and howling laughter, offering an almost cartoonish depiction of the governor as unfamiliar with and unsympathetic to the hardships facing the working poor.“Like the pharaoh of old, his heart has turned to stone,” Mr. Presley said. He also took particular delight in roasting upgrades reportedly made to the governor’s mansion, like a special shelter for lemon trees and a pricey ice maker (“It better make that good Sonic ice!”).At various stops, he has told crowds about a promise to his wife, Katelyn, whom he married just three months ago: If he wins, they will feed the homeless out of the governor’s mansion. His concern for the needy, he says, grew out his own experience enduring the turmoil and indignities of poverty. Some who came out to hear him speak recently said they were drawn to Mr. Presley because his early struggles sounded familiar — and simply because he was there, reaching out to them.“Look where he is,” said Joseph M. Daughtry Sr., the police chief in Columbus, where Mr. Presley had navigated a maze of country highways to speak to a few dozen people at a community center in a poor, largely Black neighborhood. “We have somebody who understands us,” Chief Daughtry said. “Somebody who cares about us. And somebody who is not ashamed of us.”Mr. Presley walked over to shake his hand. More