WASHINGTON — With the fate of President Obama’s health care law hanging in the balance, a lawyer for the administration faced a barrage of skeptical questions on Tuesday from four of the Supreme Court’s more conservative justices, suggesting that a 5-to-4 decision to strike down the law was a live possibility.

Predicting the result in any Supreme Court case, much less one that will define the legacies of a president and a chief justice, is nothing like a science, and the case could still turn in various directions. But the available evidence indicated that the heart of the Affordable Care Act is in peril.

The court’s decision is expected by June, and much may change as the justices deliberate and exchange draft opinions in the coming months.

If the indications from Tuesday’s arguments are correct, though, the ruling may undo parts or all of the overhaul of the health insurance system, deal Mr. Obama a political blow in the midst of the presidential election season, and revise the constitutional relationship between the federal government and the states.