Federal income tax subsidies available on the exchanges are supposed to bring premium costs below that threshold; without the credits, many people would be exempt from the individual mandate and the law would fail.

Congress assumed that most states would set up exchanges; most states, led by red-state governors, did not. Section 1321 of the law provides that when a state defaults, the secretary of health and human services shall “establish and operate such Exchange within the State.” Clear enough: “such Exchange” implies, without explicitly saying so, that the federal exchange stands in for the missing state’s exchange and assumes its functions. But another section, 1401, explicitly makes the tax subsidies available to taxpayers and their dependents who buy insurance “through an Exchange established by the State.” Those challenging the law say this means “only the state” and that the I.R.S. is not authorized to give subsidies to the more than five million people enrolled through federally run exchanges.

These two provisions, part of a 900-page statute that was cobbled together without going through the usual House-Senate conference committee in which it might have been cleaned up, are the source of the confusion. The answer to the problem, as the Fourth Circuit panel found unanimously in the King case, is obvious. It’s a basic principle of administrative law that when a federal statute is ambiguous, courts defer to the agency’s interpretation — here, the I.R.S. regulation that makes the tax credits available without regard to whether the exchange is state or federal.

The 1984 decision that established this deference principle, Chevron U.S.A. v. Natural Resources Defense Council, Inc., is so central to the modern understanding of how the government works that it is among the most often invoked Supreme Court decisions of all time, cited in some 13,000 judicial decisions so far, a number that grows at the rate of about 1,000 a year. The tax provisions of the Affordable Care Act fall so naturally onto the “Chevron deference” landscape that it would take an agenda-driven act of judicial will to keep them out and to conclude that Congress enacted a law that contained the seeds of its own destruction.

Chief Justice John G. Roberts Jr. knows something about taxes. He saved the Affordable Care Act from his usual allies two years ago by his opinion deeming the individual mandate’s penalty provision to fall within Congress’s tax power. This case puts him back under what I can only assume is an unwelcome spotlight.

It takes the votes of four of the nine justices to accept a case. Certainly Justices Anthony M. Kennedy, Antonin Scalia, Clarence Thomas, and Samuel A. Alito Jr. — the four who two years ago would have invalidated not only the individual mandate but the entire law — voted to hear King v. Burwell. (Michael A. Carvin, the plaintiffs’ lawyer, predicted as much last month, declaring in an uninhibited interview that the pending rehearing before an appeals court that has recently attained a majority of Democratic-appointed judges would be no deterrent to the justices who wanted to take the case. “I don’t know that four justices, who are needed here, are going to give much of a damn about what a bunch of Obama appointees on the D.C. Circuit think,” he told a reporter from Talking Points Memo.)

An intriguing question is whether there was a fifth vote as well, from the chief justice. I have no idea, although I can’t imagine why he would think that taking this case was either in the court’s interest or in his own; just two months ago, at a public appearance at the University of Nebraska, he expressed concern that the “partisan rancor” of Washington could spill over onto the court.