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“There was really the sense that we should play off the innovation rather than rely on a federal solution for us,” she said. “In addition, we had done a blue-ribbon commission on health care, so we had been talking about exchanges.”

For other states, setting up an exchange amounts to undermining their own cause through acquiescence to a binding, national law.

While nearly every state accepted a $1 million federal grant to explore setting up exchanges, South Carolina ended up returning most of its grant as an exploratory committee neared its final conclusion that the state shouldn’t participate in the exchange — a recommendation strongly supported by Gov. Nikki R. Haley, a Republican.

In a state dominated by Republicans, opposition runs high to the law’s expansion of federal subsidies, which raises Medicaid eligibility to 133 percent of the federal poverty level and offers Americans earning up to 400 percent of the federal poverty level partial subsidies for private insurance.

Instead, officials hope they can persuade the federal government to become more flexible in what it considers a satisfactory outcome by allowing the state to satisfy requirements with private exchanges that already operate in South Carolina. Mr. Keck said the state intends to foster an environment where these exchanges can expand and will continue to negotiate with the federal government.

“The feds will realize they can’t make this work and we should continue to push back at them and say, ‘We can make this work, this is how we’re going to do this,’ ” he said. “If you say no and continue to engage them, then you’re in negotiation with them.”

The federal government also has awarded larger grants to help states implement the exchanges and run them for the first few years. More than half of the states have accepted them — 10 of which are challenging the health care law — but they were returned by Kansas Gov. Sam Brownback and Oklahoma Gov. Mary Fallin.

A panel of Oklahoma lawmakers is deciding what to do about the exchanges. Leaders are offering mixed predictions of what course the state will choose.

State Sen. Gary Stanislaski expressed openness to an exchange for small businesses — also mandated under the law — but said there is no reason for the state to invest money in an exchange for individuals.

“Initially, it may not be in total compliance with the Affordable Care Act, but it’s in total compliance with the needs of the citizens in our state,” he said. “We’re banking on potentially two major events: the Supreme Court and No. 2, there’s an election and if we have a new president and majority of Republicans.”

But state Sen. Bill Brown said the law is the law.

“As much as we might dislike the thought of the national health care plan, it is still the law and we feel very strongly that we have a mandate of Jan. 1 of 2013 that we have to have a structure of an exchange in place and so we’re going to work to get that done,” he said.

In the end, the situation could be a bit ironic. Oklahoma and other states that are resisting implementing the health care law because they think it’s an overreach of government are risking more government control within their own borders, said Ms. Smith of Utah.

“Essentially what they’re saying is ‘We’re willing to take that chance. … We have decided that we are going to take the chance of allowing HHS to have both regulatory and budget control over our state,” she said. “I think that’s a terrible chance to take.”