As the clock ticks down before next week’s Republican primary in South Carolina, Nikki Haley is looking for any way to undermine Donald J. Trump and his commanding lead, including trying a new spin on an old line of attack: that he has a history of being disrespectful to veterans.

Ms. Haley, in her quest to close the 30-plus point gap between herself and the former president, has used his disparaging remarks about her husband’s National Guard deployment to revive the criticism that Mr. Trump has routinely disparaged military troops and veterans, a voting bloc that Republicans have long counted on for support.

At recent campaign stops in the state, Ms. Haley has resurfaced a story about Mr. Trump in which he reportedly told his former chief of staff, John F. Kelly, that Americans who died in war were “losers” and “suckers” and, during a visit to Arlington National Cemetery, reportedly said of soldiers who died abroad, “I don’t get it, what was in it for them?”

Ms. Haley’s campaign has increased its focus on the subject as recent polls show her flailing in her home state, and there is widespread doubt, even among her supporters, that she will have a strong showing. Yet in raising Mr. Trump’s past comments about military personnel, Ms. Haley may be indirectly helping the Biden campaign by reinforcing an argument against Mr. Trump it made in the 2020 election — and one that is likely to return in the 2024 general election contest.

While Mr. Trump won veteran households by about 12 points in 2020, his support among them slipped by about 14 points from the 2016 election. The drop-off could be attributed, in part, to the comments Mr. Kelly claims he made and his frayed relationships with his former defense secretaries, James Mattis and Mark T. Esper.

But Mr. Trump’s critical comments about veterans were also part of his successful 2016 campaign, during which he made light of the military service of his critics, like Senator John McCain of Arizona, and feuded with the family of a Muslim Army captain who was killed in Iraq.

Mr. Biden repeatedly attacked Mr. Trump’s attitude toward military service during the 2020 presidential campaign, particularly after The Atlantic first published Mr. Kelly’s allegations, which he confirmed late last year. After the report circulated, Mr. Biden lashed out in a fiery speech in which he called Mr. Trump’s remarks “disgusting” and said they showed that he was “not fit” to serve as commander in chief.

Mr. Biden, whose son, Beau, served in Iraq with the Delaware National Guard, has already cast Mr. Trump as disrespectful of veterans during his 2024 run. In South Carolina last month, he revisited Mr. Trump’s comments, saying impassionedly: “How dare he talk about my son and all lost to us like that? The only loser I see is Donald Trump.”

Mr. Trump has sought to defang Ms. Haley’s criticism by pointing out that she previously defended him against Mr. Biden’s accusations. On Wednesday in North Charleston, he read a social media post from 2020, nearly two years after she had left his administration, in which Ms. Haley said she had “witnessed the tremendous amount of love and respect” Mr. Trump had for the military.

“I love our military — you have a big military here — I love our vets,” Mr. Trump told the enthusiastic South Carolina crowd. “I’ve taken care of our vets like no president has ever done.” He accused Ms. Haley of flip-flopping and later boasted of his record for veterans while in office — an area in which he often overstates his success.

Ms. Haley’s criticism of Mr. Trump took shape after he insinuated on Saturday that her husband had accepted a deployment to Africa to escape her. While he did not directly take aim at Mr. Haley’s military service, he appeared to diminish its importance by questioning whether Mr. Haley had chosen deployment solely to leave her. (Maj. Michael Haley, a National Guardsman, is serving a voluntary, yearlong deployment stationed in Djibouti.)

She asserted that Mr. Trump had mocked her husband, and that when “you mock one person in the military, you’re mocking everybody,” telling audiences that Mr. Trump was “not qualified” to be president because she did not “trust him to protect” the troops. Her campaign issued a fund-raising message asking supporters to donate to a leader who understood military sacrifice, a digital ad that featured Mr. Trump’s so-called “anti-veteran record” and an open letter from more than 40 veterans that condemned his statements.

Initially one of several of her campaign’s disjointed attacks on Mr. Trump, the focus on veterans soon became a focal point. By the time she addressed a “G.O.P. Presidential Sweet Tea Stop” in Summerville, S.C., on Tuesday, Ms. Haley had seamlessly woven the criticism into her usual stump speech.

On Friday in San Antonio, home to a military base where Ms. Haley said her husband had trained, she suggested that Mr. Trump’s comments were part of “a pattern” of disrespect.

“He’s never been near a military uniform — he’s never had to lay on the ground,” she said. “The closest he’s ever come to being in harm’s way is by a golf ball as he’s sitting in a golf cart.”

But the strategy is one that may prove ineffective, despite South Carolina’s military bases and considerable veteran population. Chip Felkel, a longtime Republican strategist and Trump critic in South Carolina, said that Ms. Haley had missed an opportunity to hit Mr. Trump earlier in the campaign.

“I do think that his disparaging comments, or his attempt at innuendo, is probably not the smartest thing that he could do, but I’m not sure that it’s going to affect the outcome,” Mr. Felkel said.

That was true of several voters who attended a Trump rally in North Charleston on Wednesday and said they did not put much stock in Ms. Haley’s criticisms. “He has a tremendous amount of respect for the troops,” said Liz Knudsen, a Charleston-area resident who pointed to Mr. Trump’s legacy as president.

Tyler Jones, a Democratic strategist in South Carolina, argued that Ms. Haley was aiding the Biden campaign by making “the most effective attacks on Donald Trump,” but in Republican spaces.

Ms. Haley, who has sought to expand her coalition in part by appealing to more moderate and left-leaning voters, has drawn crowds around larger cities and along the coast but has struggled with enthusiasm in rural areas where she needs to cut into Mr. Trump’s support.

Eric Oser, a retired Navy captain from Charleston, S.C., who is backing Ms. Haley, said that he hoped that voters would send Mr. Trump a message that his comments were unacceptable, but he acknowledged that he did not expect Ms. Haley to win.

“If you’re a Democrat, this is your shot,” Mr. Oser said, urging them to back Ms. Haley. “Take a whack at Trump. Does that mean she’s going to be president? No. But it’s going to send a message.”

In a sign of Ms. Haley’s stubborn challenges in the state, while many voters at her events condemned Mr. Trump’s remarks as disrespectful, some also lamented that she had spent too much time firing back at the former president. Terry Kiser, 72, a retired law enforcement officer, said he had voted for Mr. Trump twice but had attended her event in Orangeburg on Sunday to give her a fair shake. He came away disappointed, he said.

“She got her feelings hurt when he made comments about her husband, Mike, and I understand that — to a point,” he said. “But you can’t dwell on things like that.”