While Trump's team is focused on the implications this ruling will have on the Jan. 6 case, they are also particularly interested in how this could affect his other outstanding criminal cases.

Why's that?

Trump's lawyers have an outstanding motion to dismiss the Florida classified documents case based on presidential immunity.

While it's not likely that case will go to trial before the election, the judge in that case, Judge Aileen Cannon, has indicated she wants to wait for the Supreme Court decision before she entertains that motion. And, given her unpredictability, the Trump legal team believes the ruling could give Cannon yet another avenue to throw the case's future in doubt.

The best case scenario for Trump's lawyers would be for the Supreme Court to rule he has full immunity for any actions taken while in office, which is not likely. The worst case would be that the justices uphold lower court rulings that said criminal laws apply to ex-presidents like they apply to everyone.

What do they expect? Not a full win for either side.

If the Supreme Court says its mandate could go into effect immediately, Trump's lawyers expect Judge Tanya Chutkan to get the ball rolling very soon after in the Jan. 6 case and likely schedule a briefing in the next week and a status conference once the mandate is docketed.

There would also likely be action in Florida, where Judge Cannon could move to schedule a briefing or an in-person hearing on the motion to dismiss.

-ABC News' Katherine Faulders

When the justices appeared open to the idea of some level of immunity for former presidents, it was a shock for many veteran court observers.

"It was surprising to hear, at least from some of the justices, the possibility that a president could somehow commit criminal misconduct for which they could never be held liable in court," said constitutional law expert Michael Gerhardt. "I think that has struck many people as just, up until now, inconceivable."

One point that stood out to Gerhardt was when Justice Elena Kagan pressed Trump attorney John Sauer if a president could order the military to stage a coup and be immune. Sauer said, in their view, a president could.

"The answer that she got was one of the most disturbing I've ever heard at the Supreme Court," he said.

Read more about reaction to the April arguments here.

The high court in April heard historic arguments on whether former President Donald Trump can be criminally prosecuted related to his efforts to overturn his 2020 election loss.

Trump denies all wrongdoing and insists he should have "absolute immunity" for any "official acts" while in office.

Read the five takeaways from arguments this past April.

The Supreme Court is expected to convene at 10 a.m. today.

In their dissents, both justices Sotomayor and Jackson addressed the question of whether a president would have immunity from criminal prosecution for acts of murder -- including ordering the assassination of a political rival.

In their dissents, both Sotomayor and Jackson addressed the question of whether a president would have immunity from criminal prosecution for acts of murder -- including ordering the assassination of a political rival.

When the president "uses his official powers in any way, under the majority's reasoning, he now will be insulated from criminal prosecution," Sotomayor said in her dissent. "Orders the Navy's Seal Team 6 to assassinate a political rival? Immune."

ABC News Supreme Court contributor Kate Shaw said on ABC News Live Monday that she agreed with the dissenting opinion that ordering the hypothetical assassination could be considered immune from criminal prosecution.

"In terms of the application of this immunity to very extreme scenarios like ordering an assassination, I'm not sure the majority successfully explains why this rule would not shield that kind of conduct if it's engaged in an official capacity, even if it's wildly wrong and dangerous and destructive," she said. "If that conduct is done in official capacity, I think the dissent is right on this opinion's own logic. It would be immune, and that is a genuinely chilling implication of this case."

The SEAL Team 6 assassination hypothetical was raised during oral arguments on the case in April.

Sotomayor raised it first while questioning Trump attorney John Sauer. She pointed back to an earlier exchange Sauer had in a lower court proceeding.

"I'm going to give you a chance to say ... if you stay by it: If the president decides that his rival is a corrupt person and he orders the military, or orders someone, to assassinate him -- is that within his official acts for which he can get immunity?" she asked during oral arguments.

"It would depend on the hypothetical," Sauer answered. "We could see that could well be an official act."

-ABC News' Meredith Deliso and Alexandra Hutzler