WASHINGTON >> Supreme Court justices peppered opponents of President Barack Obama’s health care law with skeptical questions during oral arguments Wednesday on the latest challenge to the sweeping legislation.

Justice Anthony Kennedy, whose vote is seen as pivotal, suggested that the plaintiffs’ argument raises a "serious" constitutional problem affecting the relationship between states and the federal government.

The plaintiffs argue that only residents of states that set up their own insurance markets can get federal subsidies to help pay their premiums.

Millions of people could be affected by the court’s decision. The justices are trying to determine whether the law makes people in all 50 states eligible for federal tax subsidies to cut the cost of insurance premiums. Or, does it limit tax credits only to people who live in states that created their own health insurance marketplaces?

During oral arguments, the courts’ liberal justices also expressed doubts. In an earlier case involving the law, however, Kennedy was on the opposite side, voting to strike down a key requirement.

A ruling that limits where subsidies are available would have dramatic consequences because roughly three dozen states opted against their own marketplace, or exchange, and instead rely on the U.S. Health and Human Services Department’s healthcare.gov. Independent studies estimate that 8 million people could lose insurance coverage.

Activists on both sides were in place outside the marble courthouse by 5:30 a.m. Wednesday. Some held placards showing how many people in each state would lose insurance if the court rules that the law does not allow subsidies everywhere.

Opponents of the Affordable Care Act failed to kill the law in an epic, election-year Supreme Court case in 2012. Chief Justice John Roberts joined with the court’s liberal justices and provided the crucial vote to uphold the law in the midst of Obama’s re-election campaign.

The new case, part of a long-running political and legal fight to get rid of the law also known as Obamacare, focuses on four words — "established by the state" — in a law that runs more than 900 pages. The challengers say those words are clear and conclusive evidence that Congress wanted to limit subsidies only to those consumers who get their insurance through a marketplace, or exchange, that was established by the state.

The administration counters that the law was written to dramatically reduce the ranks of uninsured, and that it would make no sense to condition subsidies on where people live. The phrase "established by the state," is what the administration calls a "term of art" that takes both state- and federally run exchanges. The administration also says the term cannot be read in isolation, and that other parts of the law show that subsidies should be widely available.

Both sides in the case argue that the law unambiguously supports only its position. One other option for the court is to declare the law is ambiguous when it comes to subsidies and defer to the Internal Revenue Service’s regulations making tax credits available nationwide.

Partisan and ideological divisions remain stark for a law that passed Congress in 2010 with no Republican votes. Of the judges who have ruled on lawsuits over the subsidies, Democratic appointees have sided with the administration and Republican appointees have been with the challengers.

Roberts was the only justice to essentially cross party lines with his vote in 2012. His fellow conservatives on the court voted to strike down Obamacare in its entirety.

The lawyers arguing the case Wednesday also squared off three years ago. Michael Carvin argued part of the broad challenge to the health care law in 2012. Solicitor General Donald Verrilli Jr., the administration’s chief Supreme Court lawyer, successfully defended it.

A decision in King v. Burwell, 14-114, is expected by late June.