In 2012, the chief justice of the United States, John Roberts Jr., saved the Affordable Care Act by a single, surprising vote. On Wednesday morning, the chief justice was again expected to hold the decisive vote as the Supreme Court heard extended oral argument in the latest assault on President Obama’s signature health care law.

This case will determine the fate of a law that has transformed the American health care system. But the argument provided few clues to how the justices will rule.

The chief justice remained virtually silent for the entire argument, but most of the others took predictable positions in questioning the government and the challengers. The surprise this time came from Justice Anthony Kennedy, who had voted with the dissenters from the 2012 decision that upheld the Affordable Care Act and appeared to have no interest in protecting the law.

Nevertheless, Justice Kennedy flagged a “serious constitutional problem” with the current challenge, which focuses on a single phrase — “established by the State” — embedded deep in a subsection of the act.

Michael Carvin, the plaintiffs’ lawyer, had been arguing — against all evidence and logic — that when Congress passed the act in 2010, it undermined the law’s central goal of affordable health care for all Americans by supposedly denying tax-credit subsidies to all residents in the 34 states where the federal government runs the health care exchange.

A vast majority of the more than 11 million Americans signed up under Obamacare are eligible for these subsidies, and would be unable to afford health care without them.

The absence of these subsidies would mean the collapse of the insurance markets in those 34 states — which did not for various reasons set up their own exchanges — and costs for individuals would be even higher than they were before the law passed.

This is what concerned Justice Kennedy, who has often expressed a solicitude for states’ rights: that if the law made subsidies available only on state exchanges, that would amount to the federal government coercing states to create their own exchanges or face the implosion of their health insurance markets.

Justice Elena Kagan added that if Congress had intended such an extreme result, it would not have hidden it from view. “That’s not the clarity with which we expect the government to speak when it’s upsetting federal-state relations,” she said.

When Mr. Carvin protested that the government’s brief had not made this argument, Justice Kennedy responded, “Sometimes we think of things the government doesn’t.”