The Obama administration argues that the only other provisions the court should kill in the event the mandate is stricken are revisions that require insurers to cover people regardless of existing medical problems and limit how much the companies can charge in premiums based on a person's age or health.
The justices also will spend part of Wednesday considering a challenge by 26 states to the expansion of the Medicaid program for low-income Americans, an important feature toward the overall goal of extending health insurance to an additional 30 million people.
As the arguments resumed Wednesday morning, a smaller group of demonstrators than on previous days gathered outside.
Supporters of the law held a morning news conference where speakers talked about the importance of Medicaid. And, marching on the sidewalk outside the court, supporters repeated chants they've used the past two days including "Ho, ho, hey, hey, Obamacare is here to stay." Most of their group departed not long after arguments began inside.
Opponents of the law, including Susan Clark of Santa Monica, Calif., also stood outside the court. Clark, who was wearing a three-cornered colonial-style hat, carried a sign that read "Obamacare a disaster in every way!"
"Freedom, yes. Obamacare, no," other opponents chanted.
The first two days of fast-paced and extended arguments have shown that the conservative justices have serious questions about Congress' authority to require virtually every American to carry insurance or pay a penalty.
The outcome of the case will affect nearly all Americans and the ruling, expected in June, also could play a role in the presidential election campaign. Obama and congressional Democrats pushed for the law's passage two years ago, while Republicans, including all the GOP presidential candidates, are strongly opposed.
But the topic the justices took up Wednesday only comes into play if they first find that the insurance mandate violates the Constitution.
The states and the small business group opposing the law say the insurance requirement is central to the whole undertaking and should take the rest of the law down with it.
The federal appeals court in Atlanta that struck down the insurance requirement said the rest of the law can remain in place, a position that will be argued by a private lawyer appointed by the justices, H. Bartow Farr III.
On Tuesday, the conservative justices sharply and repeatedly questioned the validity of the insurance mandate.
If the government can force people to buy health insurance, justices wanted to know, can it require people to buy burial insurance? Cellphones? Broccoli?