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.