AMNA NAWAZ: Welcome to the "News Hour."

What started a month ago as a challenge to the Trump administration's deportation policy has morphed into a full-blown battle over executive and judicial power.

For the first time, a federal judge in Washington said there is probable cause to hold the administration in criminal contempt, this after Judge James Boasberg says Trump officials defied his orders to turn around planes carrying deported migrants to a mega-prison in El Salvador.

The administration says it will appeal.

To explain what this latest order means, we're joined again by Steve Vladeck, a constitutional law professor at Georgetown University.

Steve, thanks for joining us.

So, in part of Judge Boasberg's opinion today, he wrote this -- quote -- "The court ultimately determines that the government's actions on that day demonstrate a willful disregard for its order sufficient for the court to conclude that probable cause exists to find the government in criminal contempt."

Steve, willful disregard for its order.

Is the judge saying here that the administration is not complying with his orders?

STEVE VLADECK, Georgetown University Law Center: Certainly, at least, that it did not comply, at least back on March 15 when we had those three planes of immigrants who were sent to El Salvador.

And I think one of the important notes here is that Chief Judge Boasberg, even though this is a pretty important step, it's actually still a fairly cautious one.

He's not holding anyone in contempt yet.

He's saying, I think there's probable cause to believe there's contempt.

And he wants to know more.

He wants the government to produce more information about exactly who knew what, when, about those three plane flights.

AMNA NAWAZ: So we have now had a response from the White House as well.

Communications Director Steven Cheung posted this online.

He said: "We plan to seek immediate appellate relief.

The president is 100 percent committed to ensuring that terrorists and criminal illegal migrants are no longer a threat to Americans and their communities across the country."

So, Steve, the administration will appeal.

Given that the judge here is looking for more information, what does that mean for what happens next?

STEVE VLADECK: Yes, I mean, I think we're going to see two tracks on now.

I think we're going to see the government try to appeal.

One of the tricky parts here is that, because Chief Judge Boasberg did not take that next step, did not hold anyone in contempt, not clear this is the kind of order that even can be appealed.

Not sure that the appellate court or the Supreme Court are going to want to deal with it at this juncture.

And then, if it goes forward in the district court, Chief Judge Boasberg said, hey, government, if you want to avoid all of this, you can by purging the contempt, by providing hearings, by providing the due process that was not provided to the 200-and-some-odd men who were sent off to El Salvador back in March.

Amna, that would be an easy way for the government to make this case go away.

I think it's pretty clear the White House for whatever reason wants this fight.

And so then the question is, assuming that the White House doesn't comply, doesn't purge the contempt and isn't able to get relief from the appellate courts, what happens if and when Judge Boasberg takes that next step and holds individual officials in contempt?

That will be the thing to watch for.

AMNA NAWAZ: So if you assume all of that does unfold as you laid out, what -- if the courts are meant to be the check on the executive power here, what's the enforcement mechanism for any of this?

STEVE VLADECK: So this is where things get a little complicated.

So, under the criminal contempt statute and the federal rules of criminal procedure, which I know everyone has right on their armchairs at home... the judge has the power to first ask the Justice Department to prosecute a criminal contempt of court.

I think it's safe to assume Pam Bondi's Justice Department is going to have no interest in prosecuting contempt here.

And then there's a rule in the federal rules of criminal procedure that says, in that case, the judge can appoint a private special prosecutor to try the criminal contempt.

Amna, what's tricky here is that there are some pretty serious constitutional objections to that rule.

Just a couple of years ago, two Supreme Court justices, Justice Neil Gorsuch and Justice Brett Kavanaugh, suggested that rule might not be valid.

And so I think it's going to be a question of whether, if you're Chief Judge Boasberg, if we get to that point, you push ahead anyway and appoint a private outside prosecutor to try this case, or whether by that point you have made your point.

And you hold officials in contempt.

You point out that the Justice Department's refusing to prosecute, and you say, hopefully there will be political consequences for this kind of unprecedented defiance of a federal court.

Amna, I suspect we're going to find out the answer to which of those options he pursues sooner, rather than later.

AMNA NAWAZ: Steve, I apologize for asking a big question with 30 seconds left.

But last time you and I talked, we talked about this idea of a constitutional crisis, about whether or not the president was outright defying a court order.

Back in February, you said, I don't think we're there yet.

Do you still feel the same way?

STEVE VLADECK: I think we're still not to the point where the court has ordered him to do something, and you say, nice try, I don't believe you.

But, Amna, we're getting closer.

I mean, both sides are ratcheting up the stakes.

And so I think the question is ultimately going to be one, not for Chief Judge Boasberg, but for the Supreme Court.

Can you continue to try to walk this tightrope, or at some point are you going to have to get off the fence?

And if you get off the fence, do you get off the fence in favor of the power of the courts, or do you get off the fence in favor of packing up and going home and letting the Trump administration do what it wants?

AMNA NAWAZ: Steve Vladeck, always good to speak with you.

Thank you very much.

STEVE VLADECK: Thank you.