But Virginia and 21 other states reject that argument. To succeed with such an inducement, they say, Congress would have needed to inform the states that the law included the enticement of subsidies only for those that built their own exchanges. It never did so.

“States selected among exchange options without clear notice that the choice could harm their citizens and disrupt their insurance markets,” the states said in their brief. Indeed, they said, states as diverse as Delaware, Illinois, New Hampshire and Virginia assumed that premium tax credits would be available to their citizens through the federal exchange. To deny those credits now, those states added, “would destroy state insurance markets and render the Affordable Care Act unworkable.”

A set of states dominated by Republicans — Alabama, Georgia, Nebraska, Oklahoma, South Carolina and West Virginia — argue just as vociferously that they were well aware of the inducement.

The arrangement, they said, “came as no surprise to the states” because Congress had pursued a similar approach in many social welfare programs, using money as an incentive for states to carry out federal policies.

The briefs address virtually every conceivable argument that has come up in King v. Burwell.

The chief lobby for the insurance industry, America’s Health Insurance Plans, described the subsidies as one of “three interconnected provisions” of the Affordable Care Act. The other provisions require most Americans to have insurance and prohibit insurers from denying coverage to sick people or charging them more.

If the Supreme Court eliminates the subsidies in states using the federal exchange, the group said, “it would leave consumers in those states with a more unstable market and far higher costs than if the Affordable Care Act had not been enacted.”

Without subsidies, the insurers said, “young and healthy individuals would opt out of the exchanges,” driving up premiums for the remaining consumers, including those who do not receive subsidies.