AMNA NAWAZ: President Trump spent more than three hours touting what he sees as his administration's achievements at his Cabinet meeting today.

He weighed in on everything from crime rates to Taylor Swift to prescription drugs.

But it was his comments about reinstating the death penalty for murder cases in Washington, D.C., that we will start with tonight.

Political correspondent Lisa Desjardins joins us now.

Good to see you.

LISA DESJARDINS: You too.

AMNA NAWAZ: So we should note that this comes amid his larger proclaimed crackdown on crime in Washington, D.C., but what did the president announce when it comes to the death penalty in D.C.?

LISA DESJARDINS: Let's start with exactly what the president said.

This announcement came during an unrelated part of this meeting, which was about education.

But, during that, the president interjected this announcement: DONALD TRUMP, President of the United States: Capital punishment, capital capital punishment.

If somebody kills somebody in the capital, Washington, D.C., we're going to be seeking the death penalty.

And that's a very strong preventative.

LISA DESJARDINS: A lot to pack in those 18 or so seconds -- unpack, rather.

And let me start backwards.

First of all, this idea that the death penalty itself is a deterrent, there has long been debate about that.

But the scholarship in the last 30 years has been moving away from the idea that it is a deterrent.

And there is certainly not evidence that it is in any way a strong preventative, as the president says.

No evidence for that.

Now, let's talk about what exactly is happening here.

A lot of people are scratching their heads.

It's a very serious thing the president is saying here saying that he can make all murder cases capital punishment cases in the United States capital of Washington, D.C. Now, the issue here is that, of course, Washington, D.C., does not have the death penalty right now.

The city abolished it in the 1980s.

And in the 1990s, the citizens of Washington, D.C., also voted to keep it abolished.

But it's a federal city.

And the prosecutor there is the U.S. attorney who works for the Department of Justice and works for President Trump.

He hasn't given details here, but the thinking is that that is somehow how he hopes to get this accomplished.

AMNA NAWAZ: So the president is clearly saying what he would like to see happen.

But can the president unilaterally decide that the death penalty would be the punishment for those crimes?

LISA DESJARDINS: This is the question here.

When you take apart his words, he does seem to be indicating that all murder cases in the city would become death penalty cases, even though that is not part of D.C. law right now.

So how would he do that?

Talking to experts, perhaps he would have to try and apply a federal standard somehow to city crimes.

But there is an issue there, not only with D.C. law, but with U.S. law.

The Supreme Court in the 1970s ruled that mandatory death penalty of sentences is unconstitutional.

We talked to the death penalty information center, and they said that not only would this be breaking a precedent for Washington, D.C., but, in that way, for the nation.

ROBIN MAHER, Executive Director, Death Penalty Information Center: The Supreme Court said that juries have to first consider the individual characteristics of a defendant before they make this incredibly important decision about whether they will live or die.

So, if what President Trump is talking about are mandatory death sentences, that would be unconstitutional.

LISA DESJARDINS: Now, it comes back to what you said at the beginning, Amna.

This is part of President Trump's pushing his authority on Washington, D.C., at first on law enforcement, and now over the legal system itself.

And, of course, we don't know what he intends to do, but there are many questions about whether he can.

AMNA NAWAZ: There's a lot to keep up in the Cabinet meeting.

There's another topic I want to ask you about, and that is autism and this administration's ongoing push, they say, to investigate its causes.

What did the president say about that?

LISA DESJARDINS: This really caught our attention here, an exchange between him and HHS Secretary Robert F. Kennedy.

Kennedy has promised -- he says he's been working on trying to find the underlying cause of autism.

He himself has said he thinks there may be a link to vaccines.

There is no study that has proven that.

Dozens and dozens of studies have disproven that.

But I want you to pay very careful attention to the words between him and President Trump today.

ROBERT F. KENNEDY JR., U.S. Health and Human Services Secretary: We will have announcements, as promised, in September finding interventions, certain interventions, now that are clearly almost certainly causing autism.

DONALD TRUMP: So there has to be something artificially causing this, meaning a drug or something.

LISA DESJARDINS: All right, nothing definitive here, but a very important thing to watch.

The president himself implied that there might be a drug related, which we don't have any proof of that.

And RFK saying he's found something, and he's going to announce it in September.

This raises many more questions, but we wanted to put this on the radar because it is a very serious indication of where HHS may be going.

AMNA NAWAZ: A lot more reporting on this ahead.

Lisa Desjardins, thank you so much.

LISA DESJARDINS: You're welcome.