Chad Webb, a shy 30-year-old who is enrolling people in Mingo County, said a woman at a recent event used biblical terms to disparage Mr. Obama as an existential threat to the nation. Mr. Webb said he thought to himself: “This man is not the Antichrist. He just wants you to have health insurance.”

Eventually, though, people’s desperate need for insurance seems to be overcoming their distaste for the president. Rachelle Williams, 25, an uninsured McDonald’s worker from Mingo County, said she had refused to fill out insurance forms on a recent trip to the emergency room for a painful bout of kidney stones. “I wouldn’t do it,” she said. But when she got a letter in the mail saying she qualified for Medicaid, she signed up immediately.

Uninsured people tend to be sicker and to die younger than those with insurance, and experts have reasoned that coverage should give poor Americans a better chance to improve their health. But an influential study found that lack of access to medical care accounts for just 10 percent of premature deaths in the country, compared with the 40 percent from behavioral factors like smoking and eating unhealthful food. The rest is linked to genetics, and social and environmental factors.

A widely cited experiment in Oregon offered an early look at what happens when people suddenly get Medicaid coverage. Researchers found that physical health, like obesity and the prevalence of diabetes, did not change much. But mental health improved drastically, with instances of depression plummeting. Ms. Mills said the simple relief of having coverage had helped drive away her suicidal thoughts.

Welch is a tiny town in McDowell County, a remote patch of mountains dotted by coal mines and forests logged for timber. Life expectancy here for men is just 64 years — the lowest in the country, and even lower than in Pakistan. Rates of smoking and diabetes here are nearly double the national average, and almost half the men are obese.

In communities like these, people often eat the cheapest, most convenient, food at hand.

“Poverty is short-term thinking — what can I do today to survive,” said Sister Janet Peterworth, a charity worker in Mingo County who is enrolling people.

It also costs more to live better. “Can people adopt middle-class health behaviors without being middle class?” said Adam Drewnowski, director of the Center for Public Health Nutrition at the University of Washington.