“Another slow day at the office?”

It was Thursday afternoon, and Justice Elena Kagan was settling in for a public conversation at the Library of Congress. She had agreed to it long before the Supreme Court scheduled an extraordinary special session for that morning, to hear arguments over whether former President Donald J. Trump is eligible to hold office again.

The audience laughed knowingly at this opening question, from Chief Judge Jeffrey S. Sutton of the U.S. Court of Appeals for the Sixth Circuit. Justice Kagan said the sequence of events had an upside.

“It would be impossible to make any news today,” she said, “because everybody would be focused on the morning.”

Still, the conversation had telling moments, not least because Judge Sutton is the author of two books on the role states should play in making constitutional law. Hours earlier, Justice Kagan had, by contrast, scoffed at the idea that Colorado should be able to decide whether Mr. Trump could remain on the primary ballot there.

“The question that you have to confront,” she told a lawyer for voters challenging Mr. Trump’s eligibility, “is why a single state should decide who gets to be president of the United States,” adding: “This question of whether a former president is disqualified for insurrection to be president again is, you know — just say it — it sounds awfully national to me.”

That statement, from one of the court’s liberal members, along with skepticism from a majority of the justices, suggested that Mr. Trump was likely to prevail in the case and would be allowed to stay on the ballot around the nation unless Congress acted.