AMNA NAWAZ: The Supreme Court ruled late yesterday that the Trump administration can continue to use a rare 18th century war authority to deport Venezuelan immigrants alleged to be gang members.

William Brangham is here now with more -- William.

WILLIAM BRANGHAM: Amna, the justices, which were split 5-4, effectively overturned Judge James Boasberg's earlier temporary injunction blocking those deportations.

But the court did stipulate that migrants must be given -- quote -- "reasonable time to challenge their deportations under the Alien Enemies Act."

So, to discuss this further, we are joined again by Steve Vladeck.

He's a constitutional law professor at Georgetown University.

Professor Vladeck, great to have you back on the program.

So the administration clearly believes that this decision was a victory.

The president called it a great day for justice in America.

When you look at that ruling, does it feel like a true victory for the president's immigration policy?

STEVE VLADECK, Georgetown University Law Center: So, I mean, the first answer is no.

President Trump had taken the position that he had the power to remove individuals without the kind of due process that, as you quoted, the Supreme Court majority has insisted on.

And he said he can do it without having to even justify it after the fact.

And so the fact that we're going to have hearings now, at least for anyone going forward, it's actually a pretty big loss for the Trump administration, even if it came in the process of vacating, as you note, these lower court rulings by Judge Boasberg.

WILLIAM BRANGHAM: I mean, how concerned are you that, if you're using the Alien Enemies Act to deport people, that people who are subject to deportation will have the ability to have their day in court, so to speak?

STEVE VLADECK: Yes, William, that's the right question.

And I think part of why you have seen so much disagreement today over how big of a deal yesterday's ruling was is because it really remains to be seen.

The concern that folks have is that there will be some individuals who will have access to lawyers, whose families will be able to fight for them in court, but that there might be some individuals who won't.

And so I think a lot now depends upon just how robust the individualized review that the Supreme Court contemplated actually is going to be on the ground.

And frankly, William, a lot depends on whether the Trump administration, now that it knows it has to provide this kind of individualized review, is going to actually shy away from relying upon this very old statute, which I think the original plan had been to use for mass summary removals.

And now the Supreme Court has put a pretty big obstacle in the course of that.

WILLIAM BRANGHAM: We know as part of those removals that the administration has now admitted that they mistakenly took this one man, Abrego Garcia.

An earlier judge years before had said that deporting this man back to El Salvador would be dangerous for him and had blocked that to happen.

He got swept up in this and was taken out anyway.

Chief Justice John Roberts yesterday said that a lower court's ruling that he has to be brought back is on hold for now.

The attorney general, Pam Bondi, was asked about this, and she said that Garcia ought to remain in El Salvador.

Let's listen to what she said.

PAM BONDI (R), U.S. Attorney General Nominee: He is a known gang member.

ICE testified he was a gang member, and we believe he should stay where he is.

WILLIAM BRANGHAM: I mean, it is worth noting that none of those claims that Bondi is making have been proven in a court of law.

What does this intervention, though, mean for the issue of due process for people in these cases?

STEVE VLADECK: Yes, so William, again, I mean, I know it's a frustrating answer, but I think it's going to depend on what the full court does.

I mean, what Chief John Roberts did on Monday was really just buy a little bit of time for the full court to rule on whether Judge Xinis, this federal judge in Greenbelt, Maryland, has the ability to compel Secretary Noem to take steps to try to bring Abrego Garcia back.

And this is why, again, I think we have to be a little bit tentative in our conclusions about what the Supreme Court's doing in these cases.

William, if we get a decision from the Supreme Court later this week where the court says, actually, yes, the federal courts really are powerless, that's obviously a huge win for the Trump administration, not just in Abrego Garcia's case, but with regard to the alien enemies, or at least the alleged alien enemies, who have already been removed to El Salvador.

But, in contrast, if the Supreme Court comes back and says, even folks who have been removed are entitled to use our courts to make sure the U.S. didn't do anything wrong, if that's where this ends up, I think we're going to look at these rulings as actually a bigger loss for the Trump administration and a stronger defense for the rule of law than they might seem at first blush.

WILLIAM BRANGHAM: All right, that is Georgetown Law Professor Steve Vladeck.

Always great to have you.

Thank you so much for being here.

STEVE VLADECK: Thank you.