The Supreme Court on Monday tried to discern just how vague and opaque a law must be before the justices should strike down the whole thing and tell Congress to try again.

At issue is part of the Armed Career Criminal Act that automatically provides longer sentences for those who have been convicted of three previous violent felonies. The law spelled out some things that would qualify as violent felonies — using or threatening force in connection with a burglary or arson, the use of explosives. It then added a catchall category for other crimes that might qualify: those that otherwise involve “conduct that presents a serious potential risk of physical injury to another.”

The court has looked at what is called the “residual clause” five times in the past seven years as judges have been stumped or given conflicting answers on what fits and what doesn’t. That alone should give the court pause about whether it is workable or is instead unconstitutionally vague, said Minneapolis public defender Katherine M. Menendez.

“Its vagueness is proven by this court’s inability after repeated efforts to discern a meaningful and replicable interpretive framework that will guide lower courts,” Menendez said at Monday’s oral argument .

She faced sharp questioning from Justice Samuel A. Alito Jr., one of the two former prosecutors on the court.

“Almost every case that comes here involves a dispute among the lower courts about what something means, about what the constitutional rule is or what the statutory interpretation should be,” Alito said. He added later: “Can a statute be vague simply because this court messes it up?”

But the residual clause has come in for special criticism. Justice Antonin Scalia has said in previous cases that he thought it was too vague for a law that adds 15 years to someone’s sentence.

The case before the court involved a white supremacist named Samuel Johnson. He founded the Aryan Liberation Movement, and prosecutors said he planned to fund it by counterfeiting U.S. currency. He was charged with several crimes related to firearm possession.

Johnson was subject to an enhanced sentence because he had previous convictions. But he said that one of them — mere possession of a sawed-off shotgun — should not qualify as violent.

The Supreme Court originally took the case to decide that question. But months after the first argument, apparently unable to agree about the proper disposition of the case, the justices scheduled a new hearing on whether the clause was unconstitutionally vague.

As might be expected, Scalia led the questioning of whether the law could be saved. “Can we just patch up this statute in ways that have nothing to do with its text?” he asked Deputy Solicitor General Michael R. Dreeben, representing the government. He suggested that was a job for Congress.

Scalia said he did not believe it was enough that everyone agreed that some convictions would qualify.

“I suppose you could have a statute that criminalized annoying conduct, right?” Scalia asked. “And according to the government, that would not be unconstitutional, because there’s some stuff that is clearly annoying, right?”

Dreeben said the concern should be less because the burden is on the government.

If a court is not satisfied that a crime fits within the category, “the government loses,” Dreeben said. “The tie goes to the defendant.”

The case is Johnson v. United States.