The Supreme Court appears willing to rule on the administration’s health care act, but what that ruling will be remains unclear after Tuesday’s divisive oral arguments.

Monday’s hearings dealt with whether the court could rule on the Patient Protection and Affordable Care Act (PPACA) at all, considering that the 1867 Anti-Injunction Act prohibits taxpayers from challenging a tax before it has been instituted (the PPACA’s financial penalties do not kick in until 2015). Most of the justices, however, seemed inclined to accept the government’s argument that the PPACA’s fine is a “penalty,” not a “tax” designed to raise revenue.

On Tuesday, the court heard two more hours of oral arguments. At issue was the act’s individual mandate, which would require most Americans to buy health insurance by 2014 or pay financial penalties.

Several liberal justices argued in favor of the mandate, which administration lawyers say is permitted under the Constitution’s Commerce Clause. Justice Ruth Bader Ginsburg contended that the health care market is unique, as “[t]he people who don’t participate in this market are making it more expensive for those who do.”

But the conservative members of the court expressed concern about the law’s scope. Chief Justice John Roberts worried that ruling in favor of the mandate would give the government power to regulate virtually any market. “Once we accept the principle, I don’t see why Congress’s power is limited,” Roberts said.

In light of the liberal/conservative divide, many expect Justice Anthony Kennedy to be the swing vote in the case. And his initially skeptical questioning of Solicitor General Donald Verrilli had some analysts predicting that the mandate was in trouble.

Later in the day, however, Kennedy’s questions suggested that he may be amenable to the administration’s argument that the health care industry, which nearly every person will use at some point in life, represents an exceptional case. “[T]he young person who is uninsured is uniquely proximately very close to affecting the rates of insurance and the costs of providing medical care in a way that is not true in other industries,“ Kennedy said.

How the judges rule on the individual mandate could have ramifications for the PPACA as a whole. On Wednesday, the court will hear arguments on the issue of severability, i.e. if the rest of the act can survive even if the mandate falls. It also will consider whether law’s proposed Medicaid expansion is coercive to the states.

Although oral arguments end tomorrow, a final ruling on the legislation is not expected until June, giving the country plenty of time to debate the merits of each side’s argument.

Read a full transcript of Tuesday’s hearing on the Supreme Court’s website.