Gary M. Cohen, a federal health official, said the administration “has encouraged states to establish their own exchanges.” But, he added, consumers will have access to affordable health insurance in all states, regardless of who is in charge of the exchange.

The concept of an exchange is simple: Competition will drive down prices. But operating an exchange is an immense technical challenge requiring sophisticated information technology to digest and display huge amounts of data on the costs and benefits of various insurance plans.

The federal government and states face a series of deadlines in the new year. On Jan. 1, Secretary Sebelius must determine whether each state will be able to operate its own exchange in compliance with federal standards. By Feb. 15, states must notify the federal government if they want to help with selected tasks, like consumer assistance and the supervision of health plans, in partnership with the federal government.

On Oct. 1, consumers can begin to enroll in health plans, for coverage starting on Jan. 1, 2014, when most Americans will be required to have insurance.

Administration officials said they were delighted this week when a Republican governor, C. L. Otter of Idaho, announced plans to establish a state-run exchange.

However, Mr. Otter’s rationale provided little comfort to the administration. He said he did not want to surrender power to “federal bureaucrats.” He denounced “the mandates and overreaching federal authority of the Affordable Care Act.” He said the law “will do little or nothing to reduce costs while force-feeding us coverage and increasing the size and scope of government.” And he said his decision could be rescinded if the State Legislature disagreed with him.

Pennsylvania seriously considered running its own exchange, but Gov. Tom Corbett said on Wednesday that he would not pursue the idea.