Protestors outside the U.S. Supreme Court in Washington. (Charles Dharapak/AP)

Going into Tuesday morning’s Supreme Court arguments, there was decently widespread agreement that the health reform law’s mandated purchase of insurance would survive the Court’s questioning. One poll released Monday, of 69 former Supreme Court clerks and attorneys who had argued there, found that 65 percent expected the provision to be upheld. On InTrade, odds hovered just about 67 percent.

But when the Court let out after two hours of oral arguments on the individual mandate, observers seemed a lot less certain. Jeffrey Toobin told CNN that he thought the arguments were a “trainwreck” for the administration, predicting now that the provision would get struck down. Donald Verrilli, who represented the Obama administration, stumbled over his words in his opening statement while Paul Clement, representing the law’s opponents, delivered a strong performance. On InTrade, the odds of the mandate being overturned shot up to 55 percent.

“I’ve been cautiously optimistic all along and today only pushed me a bit in that direction,” Virginia Attorney General Ken Cuccinelli told me when I caught him coming out of the Supreme Court. “I think the federal government failed to provide a constitutionality limiting principle.”

“Limiting principle” is a phrase that came up a lot in the Supreme Court Tuesday morning - 15 times, according to the transcript. It’s a legal concept you’ll probably hear a lot about in this afternoon’s analysis.

When courts review a new application of Congress’s constitutional authority, they historically wanted to see the government articulate a clear limit to those powers - they look for, in legal jargon, a “limiting principle.”

“If Justice Anthony M. Kennedy can locate a limiting principle in the federal government’s defense of the new individual health insurance mandate, or can think of one on his own, the mandate may well survive,” writes SCOTUSBlog’s Lyle Denniston. “ But if he does not, the mandate is gone.”

The core question, for Kennedy and the eight other Justices, seemed to be: if Congress could require individuals to purchase health insurance, where do the limits of power stop? Here’s one part of the arguments, where Justice Kennedy questions Verrilli particularly aggressively on the point of where, exactly, Congress’ limit of powers ends:

JUSTICE KENNEDY: Can you identify for us some limits on the Commerce Clause?

SOLICITOR GENERAL VERRILLI: Yes. The — the rationale purely under the Commerce Clause that we’re advocating here would not justify forced purchases of commodities for the purpose of stimulating demand. We — the — it would not justify purchases of insurance for the purposes — in situations in which insurance doesn’t serve as the method of payment for service.­

JUSTICE KENNEDY: But why not? If Congress —if Congress says that the interstate commerce is affected, isn’t, according to your view, that the end of the analysis.

Cuccinelli recalled Chief Justice John Roberts asking why health insurance is unique as something the government can require Americans to purchase. Justice Antonin Scalia then chimed in, asking whether the government could require Americans to exercise, a regulation that would presumably also lead to improved health.

“If you can compel people to buy health insurance because health care is unique,” Cuccinelli recalls Roberts asking, “Why aren’t there a bunch of other things that you can compel as well?”

Supporters the law agreed that limiting principle seemed to be a key issue that the Justices were grappling with the arguments.

“What they’re wrestling with, is the question of if this is allowed, is there no limit to what Congress can do under the Commerce Clause?” said Sen. Tom Harkin (D-Iowa) who attended the hearings.

He expects the individual mandate to be upheld, but does said that’s one question the Justices did not seem settled on. “I see the Court wrestling with that, and I think the answer is it depends on the time and the circumstances,” Harkin said. “Certainly no court prior to the 1930s would have upheld Social Security. But they got a new Court in, and they saw things differently.”

Could two hours of oral arguments have a big impact on the Supreme Court’s eventual ruling? There’s some reason to be skeptical: As Toobin told Ezra this morning, “Most justices say their minds are changed by oral arguments a handful of times — fewer than five — per year.” And they’re less likely to change their mind in higher profile cases, where they already have “strong views” on the issue. That being said, the health reform law could prove an exception to the rule - one of those five times - if the justices were particularly swayed by discussions of where Congressional power ends.