The official toxicology report states that Andrea Cahill’s son died at 19 years old from an accidental fentanyl overdose. But more than three years after Tyler Cahill’s death in his childhood bedroom, she doesn’t believe that. It was a poisoning, she says, and there is no question about whom to blame: “the cartels.”

Ms. Cahill believes the governments of Mexico and China should be punished for the drug’s flow into the United States. A political independent who nearly always votes for Republicans, she wants a president with relentless focus on the issue.

“It does feel like maybe nobody cares,” she said.

These days, Republican presidential candidates are working to convince people like Ms. Cahill that they share her urgency.

Ron DeSantis talks about fentanyl in every stump speech, vowing to send the military into Mexico to target cartels. Nikki Haley has promised to send special operations forces across the border. Chris Christie has called for better access to treatment. Former President Donald J. Trump has offered few specific solutions but has tapped into victims’ families’ hunger to be seen: He likens deaths from the drug to wartime casualties.

At Wednesday night’s debate, the candidates linked the crisis to immigration and foreign policy, and hammered home the toll.

“We have had more fentanyl that have killed Americans than the Iraq, Vietnam and Afghanistan wars combined,” Ms. Haley noted.

The promises are required of any politician wanting to appear in touch with New Hampshire, a state that can make or break presidential campaigns. As fentanyl has become one of the most urgent health crises in the country — it is now a leading cause of death for people under 45 — it has ravaged the small state. Last year, opioid overdose deaths hit a four-year high, though down slightly from their peak in 2017, according to state data. Most were from fentanyl.

But truly connecting with voters — persuading them that help could be on the way — is proving difficult. In dozens of interviews with people on the front lines of the fight against fentanyl, a sense of abandonment is pervasive. Many said they believed the federal government did too little to stop the epidemic from happening and that it continues to do too little to try to bring it under control.

The candidates’ talk of blockades and military intervention is met with cynicism and a deep distrust that their government can find solutions.

“I don’t see it getting better if it’s Trump or Biden or whoever is going to step in,” said Shayne Bernier, 30, who fought opioid addiction years ago and is now helping to open a sober-living home in downtown Manchester, N.H. For more than a year, Mr. Bernier has patrolled parks and streets routinely, giving information about a city-funded detox program.

Mr. Bernier grew up in the city and has “Live Free or Die,” the official state motto, tattooed on his left bicep. He considers himself a conservative. He neither loves nor loathes Mr. Trump, though he understands how the former president appeals to the anger and frustration that courses through his friends.

“They’ll talk about it for an election, and then we’ll never hear from them again,” he said of politicians’ promises to address the crisis.

Five years ago, Mr. Trump traveled to New Hampshire and remarked how “unbelievable” it was that the state had a death rate from drugs double the national average. When he promised to secure the border “to keep the damn drugs out” the audience responded by chanting: “Build that wall!”

The drugs never stopped coming in. The supply only increased, with heroin entirely eclipsed by fentanyl, its cheaper and deadlier synthetic cousin. The state is less of an outlier than it once was: In one recent public opinion poll, more than a quarter of American adults ranked opioids and fentanyl as the greatest threat to public health.

To some extent, Mr. DeSantis has picked up where Mr. Trump left off. He promises to shoot drug traffickers “stone cold dead,” a vow consistently met with applause. He largely casts the problem as a symptom of a porous border, giving conservatives another reason to rail against illegal immigration.

Tough talk about the Southern border brings some comfort to parents like Ms. Cahill. It’s unclear how her son got the drug that killed him. A video Tyler recorded and shared with a friend that night suggests he took what he believed to be Percocet to relieve pain from a recent tattoo, she says. His father found him dead the next morning.

“I had no idea how deadly it could be, how immediate — you can’t call for help,” she said. She keeps fliers in her car that warn “there is no safe experience” using street drugs.

But placing the blame on illegal border crossings is misleading. A vast majority of fentanyl in the United States enters through legal ports of entry, according to the Drug Enforcement Administration. Typically, U.S. citizens driving across the border smuggle in the drugs, stuffing them into trailers, trunks or vehicle linings.

Keith Howard, who runs Hope for New Hampshire Recovery, a peer-support community group in Manchester, grimaces when he hears candidates talk about a border crackdown as a viable solution. Mental health support, well-paying jobs and long-term treatment programs are even more important, he said.

“There is a need to escape from life for a lot of people right now,” Mr. Howard said. “The sense of alienation people have is much, much deeper than it was 10 or even five years ago.”

When Mr. Christie, a former governor of New Jersey, visited Hope for New Hampshire Recovery earlier this year, he notably did not mention the border. He served as the chair for Mr. Trump’s special commission to combat the opioid crisis, but many of the recommendations in the 138-page report that the commission issued in 2017 went nowhere. Mr. Christie blamed the pandemic, but he also said the Trump administration did not focus enough on crafting specific policies and programs.

Since then, he said, the crisis has worsened, and politicians haven’t been straight with voters about solutions.

“It’s dishonest to lead people to believe that you can enforce your way out of this problem,” he said in an interview, adding that he would support sending National Guard troops to legal ports of entry to help Border Patrol agents intercept drugs. At the same time, he added: “I don’t want to fool the American people into thinking that if I send National Guard to the Southern border, that will solve the problem.”

President Biden has focused on both expanding enforcement and improving treatment. In March, the Food and Drug Administration approved over-the-counter sales of Narcan, a nasal spray that reverses opioid overdoses. Mr. Biden has called for closer inspection of cargo and stronger penalties for those caught trafficking drugs. Recently, he criticized the Republican-controlled Congress for risking a federal shutdown, which would prevent billions allocated to the D.E.A., Department of Homeland Security and Border Patrol to address the crisis.

Victoria Sullivan considers Mr. Biden’s approach a failure. A former Republican state lawmaker in New Hampshire and political talk show host, Ms. Sullivan this year helped open a sober-living home for men in recovery.

Ms. Sullivan calls her role “government cleanup,” as she tries to fill gaps left by local agencies. She is convinced the city’s drug policies are too permissive and drawing people from around the region to Manchester’s streets. (Roughly a quarter of people who are homeless in Manchester report that they are from the city.)

Ms. Sullivan says the problem requires more aggressive interventions, accessible medical treatment, strong families and religious institutions. Her solutions hit at a contradiction in many Republicans’ views about the drug crisis: She is unabashed about her conservative, small government views, but she argues that agencies need to spend more money on rehabilitation programs.

“The government has just failed at every level,” Ms. Sullivan said. “They encourage dependence but don’t do anything near enough to get anyone on their feet on their own.”

Ms. Sullivan has voted for Mr. Trump in the past and still supports him. But she also been impressed by Ms. Haley, a former ambassador to the United Nations, who earlier this year hosted a discussion at Freedom House, the sober-living home Ms. Sullivan helped create. There, Ms. Haley promised to do more to target China’s funneling of chemicals used to create fentanyl brought into the United States.

Patrick Burns, 35, grew up in rural Maine, where he began pilfering his mother prescription opioids as a teenager. At 17, he enlisted in the Army and served for several years in Afghanistan.

When he returned in 2013, nearly everyone he grew up with was battling an addiction of some kind. He moved to Manchester partly to be closer to a larger Veterans Affairs Medical Center, thinking he could get more help there. Instead, he ran into one bureaucratic hurdle after another and said he found fentanyl all around him.

Mr. Burns voted for Mr. Trump once before and could imagine doing so again. What he finds harder to imagine, he said, is that the government that sent him to war can find a way out of the morass he sees in Manchester.

“People just don’t have a clue — it’s become such a problem,” Mr. Burns said. “Now rather than address it, they just kind of ignore it. They try to mitigate the effects, but there are not pre-emptive strikes at all. We’re just a bunch of people who have been discarded.”

Ms. Cahill has tried to ensure that Tyler is remembered. She allowed his photograph to be displayed in the Washington headquarters of the Drug Enforcement Administration, and attended a rally at the state capitol earlier this year to raise awareness.

That day, she stood with another mother in Concord, N.H., to pass out Narcan to anyone who walked by. When she offered it to two teenage boys, their father stepped in to intervene. “No thanks; they’re good kids,” she remembered him telling her, before shuffling them away.

Ms. Cahill was taken aback.

“That’s not the point,” she said, recalling the incident. “Tyler was a good kid. This stuff is out there whether we want to acknowledge it or not.”

Nicholas Nehamas contributed reporting.