The Supreme Court may have declared that the government can order Americans to get health insurance, but that doesn’t mean they’re going to sign up.

Nowhere is that more evident than Oklahoma, a conservative state with an independent streak and a disdain for the strong arm of government. The state cannot even get residents to comply with car insurance laws; roughly a quarter of the drivers here lack it, one of the highest rates in the country.

When it comes to health insurance, the effort to sign people up isn’t likely to get much help from the state. Antipathy toward President Obama’s signature health-care overhaul runs so deep that when the federal government awarded Oklahoma a large grant to plan for the new law, the governor turned away the money — all $54 million of it.

The idea that the federal government will persuade reluctant people here to get insurance elicited head-shaking chuckles at Cattlemen’s Steakhouse, an iconic old restaurant in the Stockyards City neighborhood, which is lined with street banners reading “Where the Wild West still lives.”

“That kind of frontier mentality maintains in Oklahoma, and it’s not a bad thing. It’s a good thing,” said Mark Cunningham, 64, an Army veteran having breakfast with a couple of friends in a dimly lighted booth recently. Considering the car insurance statistic, he said, “I suspect they’re going to run into the same kind of trouble on health insurance.”

Although Obama’s health-care overhaul cleared a major hurdle last month when it was upheld by the Supreme Court, the government continues to face challenges as it implements the largest social program in decades. Among the biggest is the resistance, both personal and political, that officials face as they try to achieve the law’s most ambitious goal — ­extending health coverage to 30 million uninsured Americans.

That includes people who will become newly eligible for Medicaid coverage and others who can buy insurance through new state exchanges. Beginning in 2014, most Americans will be required to get health coverage or face a fine come tax time. But it will not be a simple task to get so many people to purchase coverage, and the Congressional Budget Office estimates that, for a variety of reasons, fewer than half of the 30 million will actually gain coverage in that first year.

Hopeful advocates

Advocates believe that, when the word gets out, people will sign up because it will prove to be a good deal.

“People may have heard about ‘Obamacare’ this and ‘Obamacare’ that, and they may have even succumbed to some of the myths . . . but once people see the impact it can have on their lives, all of that is going to change tremendously,” said Ron Pollack, a health-care advocate.

Pollack sits on the board of directors of Enroll America, a nonprofit group that plans a major public relations campaign, including television and radio ads, to promote the insurance mandate and the health law in general. The group says it will focus special attention on states with large uninsured populations and those where lawmakers have actively opposed the law.

Obama officials, cognizant of the challenges, have already begun reaching out to human services organizations and government agencies that work with the poor to begin telling the un­insured about the benefits they may be able to get under the health law, such as Medicaid eligibility or subsidies to help them afford coverage.

But some in Oklahoma aren’t so sure the population here will be easy to persuade, especially if the state government continues to condemn “Obamacare.”

“If we’re not being cooperative and all the rhetoric is hostile, then that’s going to be a real barrier to providing information to people,” said David Blatt, director of the Oklahoma Policy Institute, a state policy think tank. “There’s a lot of important outreach that needs to happen before January 1, 2014, and it’s going to be extremely difficult to do that when you have state leaders standing there saying, ‘Over our dead bodies.’ ”

Resistance remains strong in other states as well, with some governors promising to opt out of parts of the law. Obama’s Republican challenger, Mitt Romney, has said he will act to repeal the law as his first priority if elected president. But it is unclear how far opponents can turn back the clock.

Many experts say the tax penalty for not having insurance — which starts at $95 and gradually increases to $695 or 2.5 percent of a person’s income — is too low to be sufficient motivation on its own.

In Massachusetts, a similar health insurance mandate enacted during Romney’s term as governor succeeded partly because it was uncontroversial, and because government agencies, nonprofit groups and health-care providers promoted it widely, even at Boston Red Sox games. Less than 5 percent of the state’s population is now uninsured.

But that was Massachusetts, a liberal-leaning state where residents are accustomed to more government regulation. No one is quite sure how it will work elsewhere.

Stubborn mind-sets

“There’s a sense in Oklahoma, and I’m not sure if this is peculiar to this state, but we don’t like people telling us what to do,” said Chuck Mai, a spokesman for AAA Oklahoma. “We know what we should do. We should buckle our safety belt every time we drive. We should drive sober. And we should have insurance on our vehicle. But having our law telling you to do those things sometimes has an adverse effect.”

Although auto insurance is required for all drivers under state law, an estimated 20 to 30 percent in Oklahoma go without it, Mai said. (In Massachusetts, about 5 percent of drivers are uninsured, the lowest rate in the country, according to the Insurance Research Institute, which last calculated the numbers in 2009.)

Lawyers and industry groups believe the low car insurance rates in Oklahoma are partly because of the sizable population of illegal immigrants. But a number of people sign up for insurance long enough to register their cars, and then, driven by poverty or a devil-may-care attitude, immediately stop paying their insurance bills.

Offenders face a $230 fine and suspension of their driver’s licenses. Police recently gained access to a database of uninsured drivers’ license plates, but the state legislature rejected a bill that would have allowed police to pull over drivers solely for insurance violations. Even the state’s insurance commissioner opposed it.

“I think that gives [the police] too much power,” said the commissioner, John D. Doak, who nevertheless considers uninsured motorists a top challenge. “I’m not a fan of the camera systems. They’ve got that in China. I want to protect people’s individual rights and liberties.”

Doak believes it will be similarly difficult to get people to sign up for health insurance.

About one in five Oklahomans lacks health insurance, also one of the highest rates in the country, despite strides made in recent years to get eligible children signed up for Medicaid. Gov. Mary Fallin (R) has been sharply critical of the new health-care law and is contemplating opting out of its expansion of Medicaid. Conservative lawmakers in the legislature are already devising ways to skirt its provisions.

Resentment and fear

Even some providers who treat the poor are skeptical. Betty Denwalt, a registered nurse at the Baptist Mission Center’s free medical clinic for the uninsured in Oklahoma City, believes people will choose not to buy insurance because they can’t afford it, or because they dislike being directed to do so by a federal government that seems disconnected from their problems.

On a recent morning at the center, patients waited in avo­cado-green chairs to pick up medicine or see a doctor. John, 37, who would not give his last name, said he could not afford health insurance for himself, his wife and his five children on his $38,000 salary as an apartment manager. He said he resents the idea that the government could compel him to do something he may not be able to afford.

“I don’t think the government should have the right to force people to do anything unless it’s following a criminal law or something,” he said.

At the Mid-Del Community Clinic across town, Mark Nelson, 46, expressed a similar sentiment. Once a successful roofing contractor, Nelson eschewed health insurance for much of his life despite suffering from a genetic kidney disease. He figured he would “sell a couple houses” if he ever needed a transplant.

His fortunes, however, took a turn just as his kidneys began to fail. He is now earning $7.50 an hour as a dishwasher at IHOP and gets most of his care at the clinic, though he eventually will need more intensive care. Yet he is still of two minds about health insurance, which he said he wishes he had, but also considers a racket.

“I’m anti-government,” he said. “Insurance is a concept based on fear.”