The Solicitor General has filed an application for a stay with the U.S. Supreme Court. The requested stay would be of a judgment entered by the U.S. District Court for the Southern District of Texas, but the real showdown here is between the Fifth Circuit and the Sixth Circuit. Last week they issued directly contrary decisions in cases about the Department of Homeland Security's September 2021 guidance about the enforcement of immigration laws. The issues include state standing, the agency's process for generating the enforcement guidance, the Section 1252(f)(1) jurisdiction-stripping provision, and universal relief (whether via a national injunction or the so-called remedy of "vacatur"). You can read the Fifth Circuit decision here, the Sixth Circuit decision here, and my recent Volokh Conspiracy post on the Sixth Circuit decision here.
This could be the big one--it could set up a Supreme Court decision about universal relief (i.e., relief that goes beyond the parties to the case, not just incidentally, but because the court is purporting to control the actions of the defendant vis-a-vis the world). Now there are various off-ramps that could mean the Court doesn't actually address whether district courts can give national injunctions or a remedy of "setting aside" agency action. For example, the agency could win on the merits, making the remedy question pointless. Or the Court could decide that the Southern District of Texas lacked jurisdiction under Section 1252(f)(1). (This kind of thing has happened several times before when the Court has granted certiorari on questions about "nationwide" relief, including Summers v. Earth Island Institute, where the cert petition was by S.G. Clement.) But if the case runs the procedural gauntlet and gets to the remedy, it would tee up the universal relief question for the Court.
General Prelogar's application for a stay is excellent. I want to add three comments: