WASHINGTON – The Supreme Court jousted for an hour Wednesday about whether the First Amendment allows the government to prosecute people for lying about earning military honors, and, if so, what else might be fair game.

Lying about whether your child received a medal? wondered Justice Samuel Alito.

Lying about the Holocaust? asked Justice Ruth Bader Ginsburg.

Lying about extramarital affairs? offered Justice Elena Kagan.

Justice Sonia Sotomayor tried out a personal example: “I take offense when someone I’m dating makes a claim that’s not true.”

At the end of the arguments in U.S. v. Alvarez, it was unclear how many of what Solicitor General Donald Verrilli called the court’s “slippery slope” questions reflected genuine concern or were simply the justices playing devil’s advocate.

The questions raise difficult issues, Verrilli conceded, but they should not keep the court from upholding the Stolen Valor Act, which makes lying about receiving some of the nation’s highest military awards and decorations a crime, punishable in some cases by incarceration.

The statute is “about as narrow as you can get,” Verrilli said, and targets with “pinpoint accuracy” only “calculated factual falsehoods.” And the government since the days of George Washington has shown an interest in promoting valor and bravery in its military and keeping “charlatans” from usurping that glory.

It seemed from the general tenor of the arguments that the justices were looking for ways to agree with Verrilli that the exception to the First Amendment’s speech protections was narrow.

He seemed to have one sure supporter in Justice Antonin Scalia, whose comments were uniformly protective of the government’s interests.

“When Congress passed this legislation, I assume it did so because it thought that the value of the awards that these courageous members of the armed forces were receiving was being demeaned and diminished” by those who falsely claimed them, Scalia said.

And Verrilli had one clear skeptic in Sotomayor.

“I thought the core of the First Amendment was to protect even against offensive speech,” she said. “You can’t really believe that a war veteran thinks less of the medal that he or she receives because someone’s claiming that they got one.”

But the rest of the court seemed more conflicted. Chief Justice John Roberts, for instance, asked Verrilli whether the government could criminalize lying about whether one received a high school diploma.

Justice Anthony Kennedy worried about the government prosecuting liars.

“It presumes that the government is going to have a ministry of truth, … and I just don’t think that’s our tradition,” Kennedy said.

On the other hand, Kennedy said, “it does seem to me that you can argue that this is something like a trademark, a medal in which the government and the armed forces have a particular interest, and we could carve out a narrow exception for that.”

There was some interest among the justices in trying to decide whether falsely claiming the honors led to a type of gain that amounted to fraud.

If the law is struck down, supporters in Congress already are preparing a version that would make it a crime to benefit from lying about being an award-winner.