Kagan recalled the first time she attended one of the conferences, limited to the nine justices, where each member says how he or she would rule in cases. Dealing with a major case, the members each gave his or view and, within 10 minutes, the tentative outcome was set. Then the justices spent 40 minutes on a less-noteworthy case before they finally arrived at a point where they could say, “O.K., we could do the case this way.”

At first, Kagan said, it seemed crazy to her to spend so much more time on a lesser case, but then she realized it made sense, given the established opinions individual justices had, the process for reaching a decision, and the prospects for persuading others. “Some cases, you’re not going to persuade each other,” she said. “But there are a lot of others where you can.”

Her description indicates that, when it comes to a case like the health care overhaul, there may not be much space for justices to persuade one another at the conference. That does not, however, mean that some elbow-twisting couldn’t happen later in the deliberations, as the justices begin drafting opinions. As one former Supreme Court clerk told me, it “It wouldn’t be unprecedented, on a case like this, for two justices to have a sort of walk in the woods” during the process.

Less pertinent, but still entertaining, Kagan also shared that she has gone hunting with her colleague Justice Antonin Scalia, who has a large animal head in his chambers named Leroy:

“Justice Scalia has made a huntress out of me,” she joked. She said the two are planning to go hunting in Montana in October. In his chambers, Scalia has a large animal head he calls Leroy, Kagan said. “He insists I’m going to shoot myself an antelope,” Kagan said. “Justice Scalia insists I need my own Leroy.”