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Originally a Republican idea, exchanges then won bipartisan support, only to be abandoned by many in the GOP once they were incorporated into Mr. Obama’s health care law.

The basic concept is that setting up a marketplace with clear-cut rules would benefit consumers and encourage insurance companies to compete, helping keep costs in check. Former Massachusetts Gov. Mitt Romney set up an exchange in that state under his 2006 health care overhaul law. And Utah already has launched one that caters to small businesses.

Under Mr. Obama’s law, plans in the new marketplaces will have to cover a set of “essential” benefits, including hospitalization, doctor visits, prescriptions, prevention, and care for pregnant women and young children. Cost to the consumer will be the main difference among plans, with four levels of coverage: bronze, silver, gold and platinum. A consumer with a bronze plan will pay lower monthly premiums, but would face higher cost-sharing for medical care.

Exchanges also will steer low-income people to state Medicaid programs. The law gives states the option to expand Medicaid to cover more of their low-income residents, with the federal government picking up about 90 cents of every dollar in added costs.

Coverage through exchange plans will begin on Jan. 1, 2014.

At the same time, the law will require most Americans to carry health insurance, either through an employer or a government program, or by buying their own policies. Insurance companies will be barred from turning away the sick or charging them more, and they also will be limited in what they can charge older customers.

• Associated Press writer John Miller in Boise, Idaho, contributed to this article.