WASHINGTON — The Supreme Court argument over subsidies that help millions of people afford their health insurance suggests that the Obama administration has two chances to attract one critical vote.

The justices will gather in private Friday to cast their votes in the case. The outcome after Wednesday’s argument appears to be in the hands of two conservative justices — one who voted with the court’s four liberals to uphold the law in 2012 and the other who joins the liberals more often, but who would have killed the whole thing three years ago.

If Justice Anthony Kennedy had his way in 2012, there would be no health care case because there would be no Affordable Care Act. Kennedy, whose vote often is decisive in cases that divide the court’s liberals and conservatives, was one of four dissenters who would have struck down the entire law.

But on Wednesday, Kennedy at least left open the possibility that he would not vote the same way again because of a legal concept known as constitutional avoidance. The idea is that judges should avoid interpreting a law in a way that raises constitutional problems if there’s any other reasonable way to view it.

The dispute focuses on four words in the massive health law, “established by the state,” which the challengers say is clear evidence that Congress intended subsidies to go only to people in states that created their own health insurance marketplaces, or exchanges. The idea was to have a carrot-and-stick approach, the challengers’ lawyer, Michael Carvin, said. Congress wanted states to establish their own exchanges and held out generous subsidies to the residents of those that did.

But Kennedy said such a scheme would raise a serious constitutional question about whether the federal government was trying to coerce the states to act.

Kennedy told Carvin that “if your argument is accepted, the states are being told either create your own exchange or we’ll send your insurance market into a death spiral.”

He repeated his concern when Solicitor General Donald Verrilli Jr. defended the administration’s view that subsidies are available everywhere because Congress did not want a law designed to reduce the number of uninsured Americans to leave people unable to afford insurance based on where they live.

If Carvin is right, “this is just not a rational choice for the states to make and … they’re being coerced,” Kennedy said. “And that you then have to invoke the standard of constitutional avoidance.”

Verrilli agreed with Kennedy that he was raising yet another reason for the court to adopt the administration’s view.

Not everything the justice said, though, cut in the administration’s favor. He told Carvin there may be no other reasonable way to read the provision at issue. “It may well be that you’re correct as to these words, and there’s nothing we can do. I understand that,” Kennedy said. He also did not sound persuaded by Verrilli’s portrayal of the law to allow subsidies nationwide.

Kennedy’s comments could give both sides reason to hope. Chief Justice John Roberts said so little that Carvin told reporters after the argument, “It would be a fool’s errand to infer anything from silence.”

Roberts disappointed Carvin and other conservatives when he cast the decisive vote in favor of thehealth care law in 2012.