Nikki Haley, fresh off another defeat by former President Donald J. Trump, brought her sputtering campaign on Sunday to Michigan, warning that even if Mr. Trump clinches the 2024 Republican nomination he has too much baggage to win in November.
In a rally north of Detroit, just a day after a 20-point loss in South Carolina, her own home state, Ms. Haley continued to spin her defeat as a troubling sign not for herself but for her opponent, saying that she represented a significant 40 percent of Republican voters that the incumbent president could not tear away. (The latest results from South Carolina’s primary show her finishing at 39.5 percent to Mr. Trump’s 59.8 percent.)
“You can’t have a candidate who’s going to win a primary who can’t win a general,” she insisted to nods of approval and applause from hundreds of people packed into a hotel ballroom in Troy, Mich.
The general election pitch is one that Ms. Haley has been making for months — and one that could prove potent in Michigan, a battleground state. But Ms. Haley is facing an uphill climb in Michigan, just as she is in the other swing states that she is expected to visit this week ahead of upcoming primary contests.
Mr. Trump narrowly lost Michigan to Joseph R. Biden Jr. in 2020 after a presidential term alienating independents and suburban women, the segments of the electorate that make up a strong part of Ms. Haley’s small but not insignificant base. And her campaign has counted the state as one of more than a dozen that are critical to her path to the nomination because they have primaries not limited to registered Republicans.
But the difficulty for Ms. Haley in Michigan, which holds its primary on Tuesday, is similar to that in the early-voting states: She’s running for the Republican Party’s presidential nomination, and the base is sticking with him. The strength she has shown with more moderate voters, even Democrats, has not been enough to overcome his significant advantage.
Richard Czuba, an independent pollster in Lansing, Mich., said the state had a long history of Republican and Democratic voters crossing over in presidential primaries to upend contests and send a message. But he predicted little chance of that for Ms. Haley. The results of the state’s Republican primary this year are seemingly such a foregone conclusion, mostly thanks to Mr. Trump’s dominance, that his polling firm had even stopped bothering to survey voters, he added.
“There is no race,” he said.
Ms. Haley’s campaign began running its first television advertisements in the state only last week, targeting the Detroit area with part of what her staff said was a half-million-dollar buy in the state. Her allied super PAC reported spending another half-million for ads in the Michigan market as of Saturday, according to federal filings.
Ms. Haley arrived in the state with little to no momentum. While she has continued to amass donations — she collected $1 million from grass-roots supporters in less than 24 hours after her loss in the South Carolina primary, according to her campaign — Americans for Prosperity Action, the political network created by the billionaire industrialist Koch brothers, announced on Sunday that it would no longer be spending in support of her run. Ms. Haley is expected to hold more fund-raisers while on her cross-country campaign swing this week.
In interviews on Sunday, many of Ms. Haley’s supporters said they were grateful that she was keeping up the fight. Some were fed up with Mr. Trump’s grip on the party and on Michigan Republicans, and they worried that his mercurial nature and slew of legal troubles did not bode well for the future of the nation. None of them wanted a Trump-Biden rematch in November.
“Trump’s in a huge amount of problems just in the courts,” said Denise McDonald, 65, a retired pensions plan manager, “and both he and Biden walk a fine line just by their age.”
Onstage, Ms. Haley echoed Mr. Biden’s promises during the 2020 presidential election to return normalcy to U.S. politics if elected, saying that she was “talking about the heart and soul of our country.” As she has since the field winnowed to two candidates, from more than a dozen, she continued her sharp attacks on Mr. Trump, criticizing him over increasing the national debt, warming up to dictators, promoting an isolationist foreign policy and seeking to influence the Republican National Committee.
“He’s not going to get the 40 percent by trying to take over the R.N.C. so that it pays all legal fees,” she said. “He’s not going to get the 40 percent if he is not willing to change and do something that acknowledges the 40 percent. And why should the 40 percent have to take to him?”
Her loss in South Carolina on Saturday was her first ever in the state, where she rose to become its first female governor. Though she outperformed the polls there, drawing just below 40 percent of the vote, she still did not meet her own benchmark: She did not do better than the 43 percent support she received in New Hampshire in January. In her election night speech and in a video released Sunday, pledging to keep up the fight, Ms. Haley argued the percentages were about the same, casting herself as the voice for the people seeking an alternative to a Trump-Biden rematch.
Polls in the states she is expected to visit this week, including Colorado, Minnesota, North Carolina, Utah and Virginia, show her lagging far behind Mr. Trump.
Hours before the last ballots were cast in South Carolina, Ms. Haley appeared to suggest a winding down could be in sight.
“We’re going to keep going all the way through Super Tuesday,” she told reporters in Kiawah Island, where she voted with her family at a polling station inside a gated community near her home. “That’s as far as I’ve thought in terms of going forward.”
Michigan will award only 16 of 55 delegates based on the results of its primary on Tuesday. The rest will be allotted at its convention on Saturday in a process likely to advantage Mr. Trump.
The state will make for an interesting backdrop. Mr. Trump focused on the voting in Michigan in his efforts to subvert the 2020 election. He won the state by nearly 11,000 votes in 2016, and lost it to Mr. Biden by more than 150,000 votes in his 2020 re-election bid. Mr. Trump has since maintained a chokehold on the state’s Republican Party, as it has fallen into a political maelstrom of warring factions.
Dennis Darnoi, a longtime Republican strategist in Michigan, also rejected the idea that Democrats and left-leaning independents could help Ms. Haley when they have their own competitive contest. Liberal groups have been calling for a protest vote against President Biden over his response to the war between Israel and Hamas. Democratic supporters of the president have been pushing back.
Mr. Darnoi recalled that the Haley campaign initially appeared to be sending many texts to the state’s prospective voters but noted that the communication had dropped off and become intermittent. Her ground game has been “fairly nonexistent,” he said.
“The Michigan primary voter is very supportive of Donald Trump. They are very excited to vote for him,” Mr. Darnoi said, adding that there did not seem to be a lane for anyone else.