A sweeping new Texas law that would empower state and local police officers to arrest migrants who cross into the state from Mexico without authorization faces an uncertain future.

On Tuesday, the U.S. Supreme Court briefly cleared the way for implementation of the law, which the Biden administration has challenged as an unconstitutional infringement on the federal government’s power to set and enforce immigration law.

But when the justices returned the case to an appellate court to decide whether a district court’s block of the law should stand while the challenges made their way through the legal system, the appellate court promptly dissolved its own earlier order allowing the law’s enforcement during the process. That put the law on hold once again — for the moment.

The appellate court has scheduled hearings on the issue for Wednesday morning.

Critics say the law could lead to the detention of people hundreds of miles from the border, if police officers suspect that they are in the country illegally. It would certainly allow Texas to expand the border security measures that it has put in place on private land along the border, including barriers of razor wire, National Guard troops and a buoy barrier in the Rio Grande.

The actual case over who ultimately has jurisdiction will continue to play out in the courts, with far-reaching implications for immigration enforcement in the United States.

A Federal District Court judge in Austin temporarily blocked the law from going into effect on March 5. The judge ruled that the statute ran afoul of federal law and the U.S. Constitution. In issuing a preliminary injunction, the judge found that Texas would very likely lose the case on the merits.