The case arose from a lie told in 2007 at a public meeting by Xavier Alvarez, an elected member of the board of directors of a water district in Southern California. “I’m a retired Marine of 25 years,” he said. “I retired in the year 2001. Back in 1987, I was awarded the Congressional Medal of Honor. I got wounded many times by the same guy.” That was all false, and Mr. Alvarez was prosecuted under a 2005 law, the Stolen Valor Act, which makes it a crime to say falsely that one has “been awarded any decoration or medal authorized by Congress for the armed forces of the United States.” Mr. Alvarez argued that his remarks were protected by the First Amendment. His case ran into trouble at the Supreme Court as it emerged that many justices accepted two fundamental propositions. First, most of the justices seemed to accept that the First Amendment does not protect calculated falsehoods that cause at least some kinds of harm. Second, there seemed to be something like a consensus that the government has a substantial interest in protecting the integrity of its system for honoring military distinction. To arrive at those two propositions, the justices worked through any number of hypothetical questions and worried about the collateral damages to free speech values that a ruling upholding the law might generate. Justice Stephen G. Breyer said it was all right to lie, for instance, when asked, “Are there Jews hiding in the cellar?” Justice Samuel A. Alito Jr. suggested that it was acceptable to punish a false statement that “your child has just been run over by a bus.” Justice Sonia Sotomayor asked about false statements made while dating. Justice Elena Kagan asked about lies concerning extramarital affairs. Chief Justice John G. Roberts Jr. asked whether Congress could make it a crime to lie about having a high school diploma. Solicitor General Donald B. Verrilli Jr. responded that some states had indeed enacted laws concerning diplomas from public universities, and he indicated that they would be constitutional if they concerned calculated lies about verifiable facts that led to real harm. Mr. Verrilli listed several laws that punish those kinds of falsehoods, including ones prohibiting false statements to federal officials and banning the impersonation of federal officers, as well as perjury. Similarly, he said, the Stolen Valor Act punishes only knowing falsehoods that result in “the misappropriation of the government-conferred honor and esteem,” which he called “a real harm and a significant harm.” The hardest hypothetical question for the justices seemed to concern state laws that make it a crime for politicians to lie in some settings. Mr. Verrilli said such laws might run afoul of the First Amendment because of their potential to chill truthful speech for fear of prosecution. Justice Kagan asked a lawyer for Mr. Alvarez, Jonathan D. Libby, whether the Stolen Valor Act posed the same problem. “What truthful speech will this statute chill?” she asked. Mr. Libby’s response seemed to surprise Justice Kagan. “It’s not that it may necessarily chill any truthful speech,” he said. “We certainly concede that one typically knows whether or not one has won a medal or not.” Justice Kagan considered what she had just heard. “So, boy, I mean, that’s a big concession, Mr. Libby,” she said. Mr. Libby also acknowledged that the government may punish false speech that is intended to obtain something of value. Chief Justice Roberts asked whether Mr. Alvarez, who was politically active, benefited from his lie. Mr. Libby said that was possible. The chief justice said this, too, was “an awfully big concession.” Justice Anthony M. Kennedy seemed to summarize the court’s conflicting impulses in the case. On the one hand, he said, the government should not establish “a Ministry of Truth.” On the other, he said of lies like Mr. Alvarez’s, “I have to acknowledge that this does diminish the medal in many respects.” The New York Times Company and other news organizations filed a brief supporting Mr. Alvarez in the case, United States v. Alvarez, No. 11-210. The brief argued that most false statements are better addressed by exposing them in the marketplace of ideas than by punishing them as crimes. There was universal agreement on one point at Wednesday’s argument. No one spoke up for Mr. Alvarez, including his lawyer. “Certainly, people are entitled to be upset by these false claims,” Mr. Libby said. “I mean, I’m personally upset by these false claims.”