WASHINGTON — The Supreme Court on Wednesday seemed unsympathetic to the claims of a protester who said his free speech rights had been violated when Secret Service agents protecting Vice President Dick Cheney arrested him after he made critical remarks about the Bush administration’s war policies.

Even some of the court’s more liberal justices said Secret Service agents and others charged with protecting the nation’s leaders must have breathing room in assessing potential threats. The question that appeared to divide the justices was whether all law enforcement officials should be protected from lawsuits alleging that arrests were made in retaliation for speech protected by the First Amendment.

A lawyer for the agents, Sean R. Gallagher, characterized the core question in the case this way: “The issue before the court today is whether Secret Service agents who are prepared to take a bullet for the vice president must also be prepared to take a retaliatory arrest lawsuit, even when they have probable cause to make an arrest.”

David A. Lane, a lawyer for the protester, Steven Howards, said that “there is no reason to put some different rule down on the Secret Service” when First Amendment rights are involved.