Ms. Haley, the former governor of South Carolina, has won tough races in her home state. But as she vies for the 2024 Republican nomination, her state and party look different.In 2016, as Donald J. Trump was romping to victory in her home state, Gov. Nikki Haley of South Carolina backed Senator Marco Rubio as the fresh face of a “new conservative movement that’s going to change the country.”Now, Ms. Haley insists, she is that new generational leader, but even in her own state, she is finding Mr. Trump still standing in her way. If she is to make a real play for the Republican presidential nomination, South Carolina is where Ms. Haley needs to prove that the party’s voters want to turn the page on the Trump era — and where she has predicted that she will face him one-on-one after strong showings in Iowa and New Hampshire.“Then you’ll have me and Trump going into my home state of South Carolina — that’s how we win,” she told a crowd gathered inside a rustic banquet hall during a recent campaign stop in rural Wolfeboro, N.H.But Ms. Haley’s road to victory on her home turf will be steep. Ever since the state set Mr. Trump on a glide path to the G.O.P. nomination seven years ago, he has solidified a loyal base. The candidate who upended the state’s politics from outside the political system now has a tight hold on most of the Republican establishment, appearing recently with both Gov. Henry McMaster and Senator Lindsey Graham and boasting more than 80 endorsements from current and former officials across the state.“It is still clearly Trump’s party,” said Scott H. Huffmon, the director of the statewide Winthrop Poll, one of the few regular surveys of voter attitudes in the state. “That makes many Republican voters Trump supporters first. She has to remind them the party is bigger than one man.”Ms. Haley attempted to make that case on Wednesday on the national debate stage, where rivals intent on blunting her rise made her a target and put her on defense. She promised her approach would be different from Mr. Trump’s. “No drama, no vendettas, no whining,” she said. While Gov. Ron DeSantis of Florida has staked his bid on Iowa and former Gov. Chris Christie of New Jersey has gone all in on New Hampshire, Ms. Haley’s campaign officials say they have sought to spend equitable time and resources in all three early-voting states.Her campaign has its headquarters in Charleston, and is bolstered by what the campaign said was hundreds of volunteers. (The campaign declined to give specifics on staffing and volunteer efforts across all three states.)But Ms. Haley’s efforts have so far been less pronounced in South Carolina. She has spent 58 days campaigning almost evenly between Iowa and New Hampshire, but only 12 in her own backyard. Her campaign has not yet released a full list of endorsements within the state, though several key state legislators and donors are expected to back Ms. Haley in the coming days, according to her campaign. A $10 million advertising effort, more than $4 million of which has been reserved on television so far, is expected only in Iowa and New Hampshire.Ms. Haley’s campaign officials and allies argue she still has time to make up ground, even as Mr. Trump remains dominant nationwide and in all the early states, where surveys indicate he leads his nearest opponent by double digits. Former Vice President Mike Pence and Senator Tim Scott, a fellow South Carolinian, have dropped out of the race, which has helped Ms. Haley with money and momentum and tightened the fight with Mr. DeSantis for second place.At an energetic town-hall event last week in Bluffton, S.C., Katon Dawson, an adviser for the Haley campaign in South Carolina and a former chairman of the state Republican Party, pointed to the audience of more than 2,500 people — her largest crowd yet in her home state — and said the mailing lists generated from such events would help elevate her ground game.“When South Carolina jumps into focus, it’s going to jump in the gutter, and we’ll be ready for it,” Mr. Dawson said, suggesting he expected the attacks on Ms. Haley to become uglier closer to the January contests in Iowa and New Hampshire.Plenty of the attendees at the Bluffton event were former Trump supporters. Michelle Handfield, 80, a volunteer at a correctional institute, and her husband, John, 81, a retired photographer, said they had been some of Mr. Trump’s most enthusiastic admirers. Ms. Handfield, a former Democrat, said he was the first Republican she had ever voted for in 2016.Now, however, they were planning to vote for Ms. Haley for reasons similar to what the former South Carolina governor has articulated: “Chaos follows him.”“I think he was a great president, but they were after him from the beginning — the Democrats — and then he didn’t help by what he says and does,” Ms. Handfield said. “I really wish he had won a second term, but I think now he would do more harm for the country than good.”Former President Donald J. Trump has solidified a loyal base in South Carolina, appearing recently with Gov. Henry McMaster at a University of South Carolina football game.Chris Carlson/Associated PressStill, many of the state’s Republican primary voters remain ardent supporters of Mr. Trump, even as he has so far kept a light campaign schedule.“It is fascinating that we see all of these campaigns in the various stages of grief as President Trump continues to dominate the primary field,” said Alex Latcham, Mr. Trump’s early states director. “Right now, Haley is in the bargaining stage.”Ms. Haley’s political base in the state remains the same as it was when she was governor: the affluent — and more moderate — Republicans along the coast and in Charleston.But her grip on the Midlands, honed by her years in government, has loosened with time, and whatever support she had in the much more conservative Upstate around Greenville has dissipated sharply. To prevail, she must win back some of those conservatives and soften enthusiasm for Mr. Trump, all while fending off attacks from other opponents.On the debate stage Wednesday, Mr. DeSantis took aim at her conservative record as governor, saying he had signed a bill criminalizing transgender people for using bathrooms in public buildings that do not correspond to their sex at birth and argued she had not supported a similar measure. Ms. Haley countered that such legislation wasn’t necessary at the time, adding that she had not wanted to bring government into the issue. The South Carolina bill did not advance past its introduction in the State House.Last week, Mr. DeSantis also ripped into Ms. Haley as he campaigned in South Carolina. On Friday, he appeared with Tara Servatius, a popular radio broadcaster on the Greenville station WORD, who has been using her show for weeks to blast Ms. Haley as an untrustworthy moderate.“For the last 10 years, I have tried to get Nikki Haley to come answer unscripted questions,” Ms. Servatius said, to which Mr. DeSantis quipped, “Good luck with that.”Some Republican primary voters seem to be looking for a figure who embodies more drastic conservative change. Tim Branham, 73, of Columbia, could not recall much that Ms. Haley accomplished as governor. “In my opinion, the best thing you can say about Nikki was she’s a Republican,” he said.Still, Ms. Haley continues to pull in key endorsements along with a fresh wave of big-money donors looking for a Trump alternative, strengthening her finances as well as her field operations.Within a week of endorsing her campaign, Americans for Prosperity Action, the political network founded by the billionaire industrialist brothers Charles and David Koch, had already poured $3.5 million into hiring door knockers, placing digital ads and producing door hangers and media in Iowa and South Carolina, according to federal spending filings. Within a day of its announcement, Americans for Prosperity Action had more than 140 volunteers and staffers already out in nearly half of South Carolina’s 46 counties spreading her message.Kyle Kondik, an elections analyst at the University of Virginia Center for Politics, said Ms. Haley’s appeal, which appears greater among college-educated Republicans who do not think of themselves as particularly religious, better positioned her for success among Republican primary voters in New Hampshire.But he added that a more telling test of how her message might fare among Republican primary voters in South Carolina would be Iowa and its largely white and Christian evangelical Republican base — a group that is closely aligned with Mr. Trump.“If Haley loses South Carolina, that very well may be curtains,” Mr. Kondik said.Shane Goldmacher More