AMNA NAWAZ: Welcome to the "NewsHour."

On the very last day of arguments, the U.S. Supreme Court heard debate over one of its most consequential cases, whether a former president is immune from prosecution for official actions taken while in office.

Outside the court this morning, protesters gathered dressed as kangaroos and holding signs reading things like "Trump is not immune."

Inside, arguments were heard on an appeal brought by former President Donald Trump, who's being prosecuted by special counsel Jack Smith for attempting to overthrow the results of the 2020 election.

John Yang is here now in studio with more -- John.

JOHN YANG: Amna, it was a big day for former President Trump in a number of courts.

In addition to the nearly three hours of oral arguments in his immunity case at the Supreme Court, a grand jury in Arizona indicted several of his closest allies for allegedly trying to subvert the 2020 election.

Following all of this is the "NewsHour"'s William Brangham and our Supreme Court analyst, Marcia Coyle.

They were both in the Supreme Court this morning.

Marcia, remind us the basics.

What is President Trump's argument and what's the government's response?

MARCIA COYLE: OK, John, very simply, President Trump is asking the court to say that a former president has absolute immunity for conduct involving his or her official acts, and that that immunity stretches all the way to the outer perimeter of his office.

And he's looking to certain clauses in the Constitution and certain precedents to bolster that argument.

But the government is saying, basically, there is no immunity clause in the Constitution.

It does not extend to the president's official acts, although the government said today there is a small core group of powers that are in Article 2 of the Constitution, like the pardon power, the veto power, that are off-limits to criminal law.

JOHN YANG: And, William, the justices spent a lot of time today distinguishing or exploring how to distinguish between a private act and a public act.

And we have got Justice Elena Kagan posing a hypothetical to one -- to Trump's attorney.

ELENA KAGAN, U.S. Supreme Court Associate Justice: He was the president.

He is the commander in chief.

He talks to his generals all the time.

And he told the generals, I don't feel like leaving office.

I want to stage a coup.

Is that immune?

D. JOHN SAUER, Attorney For Donald Trump: If it's an official act, there needs to be impeachment and conviction beforehand because the framers viewed the risk -- that kind of very low risk... ELENA KAGAN: If it's an official act.

Is it an official act?

D. JOHN SAUER: If it's an official act, it's impeach... (CROSSTALK) ELENA KAGAN: Is it an official act?

D. JOHN SAUER: On the way you described that hypothetical, it could well be.

I just don't know.

You would have to -- again, it's a fact-specific context which would be the determination.

(CROSSTALK) ELENA KAGAN: That answer sounds to me as though it's like, yes, under my test, it's an official act.

But that sure sounds bad, doesn't it?

D. JOHN SAUER: Well, it certainly sounds very bad.

JOHN YANG: William, why is this question so important?

WILLIAM BRANGHAM: Well, as Marcia was just describing, this is trying to delineate what's prosecutable and what is not.

And a private act, one that has nothing to do with your official duties as president, if it's criminal, you can be prosecuted.

I mean, if you're dealing narcotics out of the White House, no one's going to argue that that should not be prosecuted.

An official public act is very different, and that's what the heart of this case was all about.

And this gets to the heart of Trump's argument, which is that, in all of the things that the DOJ alleges he was doing that they argue is a conspiracy to subvert the election, he says, no, that was just part of my talking to the Department of Justice, talking to state elections officials to root out any potential fraud that we were concerned about, and that that's not illegal, first, and that because I was doing it as president, I should be immune from it.

And so that is the argument they have been making, and that's where the fight today really rested.

JOHN YANG: Marcia, what else do the justices seem to be concerned about?

MARCIA COYLE: Well, there was some concern that the criminal laws might be used by political opponents of former presidents to go after them for decisions they made or acts they took.

There was concern that presidents were -- or knowing that there's no immunity, might actually pardon themselves for everything before they leave office.

But, most importantly, I think there was concern about whether there would be a chilling effect on a president doing his or her duties if there is no immunity at all for official acts.

JOHN YANG: And two justices, Samuel Alito, a conservative, and Justice Ketanji Brown Jackson, one of the liberals, sort of talked about this from different viewpoints.

MARCIA COYLE: Very different viewpoints.

SAMUEL ALITO, U.S. Supreme Court Associate Justice: If an incumbent who loses a very close, hotly contested election knows that a real possibility after leaving office is not that the president is going to be able to go off into a peaceful retirement, but that the president may be criminally prosecuted by a bitter political opponent, will that not lead us into a cycle that destabilizes the functioning of our country as a democracy?

MICHAEL DREEBEN, Advocate For Special Counsel Jack Smith: I think it's exactly the opposite, Justice Alito.

There is an appropriate way to challenge things through the courts with evidence.

If you lose, you accept the results.

That has been the nation's experience.

KETANJI BROWN JACKSON, U.S. Supreme Court Associate Justice: You seem to be worried about the president being chilled.

I think that we would have a really significant opposite problem if the president wasn't chilled.

If someone with those kinds of powers, the most powerful person in the world, with the greatest amount of authority, could go into office knowing that there would be no potential penalty for committing crimes, I'm trying to understand what the disincentive is from turning the Oval Office into the seat of criminal activity in this country.

JOHN YANG: So, Marcia, what's next?

MARCIA COYLE: Well, a decision at some point.

My sense overall was that the court doesn't seem inclined to buy Mr. Trump's argument for absolute immunity.

And if that's the case and they start trying to delineate, as William said, between official acts and private acts, what kind of tests should be applied to do that, they may well send it back to the lower courts to apply it to Mr. Trump's situation.

Now, the hardest cases that are argued in April generally aren't decided until the end of the term, which would be late June, maybe even early July.

But the Supreme Court sets its own schedule.

And there's been a lot of talk, discussion, briefs urging the court to act quickly here so that the trial may get under way at some point before the election.

So I think we just have to wait now, John, and see what happens.

JOHN YANG: And, William, what does that timing, what does it potentially do to former President Trump's trial?

WILLIAM BRANGHAM: Well, as Marcia is saying, it's all in the matter of not just how the court rules, but when they rule, because they could still rule in Trump's favor and say, you do not have blanket immunity, as you're arguing.

But when they issue that ruling, whether they push it back down to the lower courts or whether they just take a long time, if you look at the calendar, if they rule, what, the end of June, early July, Judge Tanya Chutkan has said her case needs about three months before that trial could start for lawyers to catch up on motions and things like.

That -- if that starts three months later, that is pushing that trial date right at the heart of the election, perhaps it's October or November, and there will be a great deal of pressure on her to not run a -- not run a case right in the middle of an election.

JOHN YANG: William, I want to ask you about the indictment in Arizona that we mentioned at the top of the introduction.

A grand jury in Arizona returned charges late yesterday against 18 Trump allies for conspiring to overturn the 2020 election results with a fake electors scheme.

They include former Chief of Staff Mark Meadows, attorneys Rudy Giuliani and John Eastman, and the indictment refers to Trump as Unindicted Co-Conspirator No.

1.

Here's Arizona Attorney General Kris Mayes: KRIS MAYES (D), Arizona Attorney General: The scheme, had it succeeded, would have deprived Arizona's voters of their right to have their votes counted for their chosen president.

It effectively would have made their right to vote meaningless.

JOHN YANG: So, William, what exactly are they charged with doing?

WILLIAM BRANGHAM: So, this is 18 people who are charged with conspiracy, fraud and forgery, just as you mentioned, which is all going back to their alleged efforts to deny the fact that Joe Biden won Arizona and Donald Trump did not.

It's the seven Trump aides and lawyers that you mentioned, but also 11 of these other people who signed up to be what we have now called fake electors.

These are people who knew that Trump had not won, but they stood forward and signed documents saying, we will go to Washington, D.C., and cast Arizona's electoral votes for Donald Trump, which he did not win.

And so they are being charged with part -- of being part of this scheme.

As you mentioned, Trump is not named in this charge, but Arizona has now joined four other states that are pursuing similar cases like this at the local level.

JOHN YANG: William Brangham, Marcia Coyle, thank you very much.

MARCIA COYLE: Thank you, John.

WILLIAM BRANGHAM: Thanks, John.