Outside, there were hundreds of demonstrators on both sides of the issue.
And people have been camping out for days, hoping to get a seat inside the courtroom.
Many here are watching the case closely, too, because they have a personal stake.
At work, Stephanie Perez Jarmul helps low-income mothers-to-be improve their health.
But when this social worker was going from college to grad school, and expecting her first child, her college health insurance ran out, and she'd have till open-enrollment to get on her husband's policy.
She was turned down by every company she tried.
"I was denied because I had a pre-existing condition. I was pregnant," she told Action News.
Experts tell us that's become a fairly common occurrence.
Stephanie eventually got insurance - for 500 dollars a month.
"Any of the money we had for rainy-day money was used for that," she said.
26 states, including Pennsylvania, are leading the legal battle that brought this case all the way to the Supreme Court.
They are challenging the constitutionality of requiring individuals to have health insurance by 2014 or pay a penalty.
Sen. Mitch McConnell, R-Kentucky, says, "If the court upholds that, could the federal government then order you to eat carrots? Could it order you to quit smoking?"
But Dr. David Grande - a doctor and policy expert at Penn - says the law would extend insurance to 30 million more Americans, and control costs by putting more healthy Americans into the insurance pool.
"If all you have is sick people in an insurance program, the costs get really high, and insurance is more and more out of reach of the people," he says.
Some parts of the reform law, such as prescription drug help for Medicare seniors, and allowing young adults to stay on their parents' insurance longer, are already in effect.
Grande says if the court rules against the mandate to buy insurance, other parts of the 2-year-old law may not survive, and costs could speed upward again.
"Middle class working people are simply not going to be able to afford insurance as healthcare gets more expensive," he notes.
The arguments wrap up Wednesday.
Even the experts are split on which way the court will go. But a decision is expected in June, in the midst of the presidential campaign.
