The court, however, could refuse to even consider the appeal, the first post-Sept. 11 anti-terror case to reach the justices.
Meanwhile, another measure - this one ordered by the Transportation Security Administration - has come under fire by civil liberties groups and prompted legal scholars to question whether random searches of vehicles at airport terminals violated states' rights, the Washington Post reports.
The American Civil Liberties Union and other organizations asked the court Tuesday to consider the boundaries of a law that gave the government broader spying authority after the terrorist attacks.
The ACLU argued that a review court misinterpreted the Patriot Act, making it too easy for the government to get permission to listen to telephone conversations, read e-mail or search private property, then use the information in criminal cases.
Critics worry there are not enough checks to ensure the government's snooping doesn't stretch to law-abiding citizens.
The court may not allow the appeal because the ACLU was not one of the parties in the review court case. The ACLU filed arguments opposing the government but was not directly involved.
The ACLU and Arab-American groups argue that they represent people who are being monitored under warrants approved by the super-secret Foreign Intelligence Surveillance Court, or "spy court." The court deals with intelligence requests involving suspected spies, terrorists or foreign agents.
"The irony is no one can know for certain whether they are the subject of these secret surveillance orders because they're secret," said Ann Beeson, ACLU's associate legal director.
She said the ACLU has "taken this somewhat radical step" to protect those people.
Washington lawyer Stewart Baker, former general counsel for the National Security Agency, said the groups can argue that this is the Supreme Court's best, and possibly only, chance to consider the work of the surveillance court.
Still, he said, "I can't imagine why the Supreme Court would take this case. The court doesn't take cases that are unique."
Scott Silliman, director of Duke University's Center on Law, Ethics and National Security, said the Supreme Court would have to make an extraordinary exception. "Clearly it will be dismissed," he said.
The November ruling by the review court was a huge victory for the Bush administration, which argues that the surveillance is an important component of its war on terror.
The administration was the only participant in the case. The Justice Department had appealed after the spy court turned down a request for a wiretap. The review court overturned that decision. It was the first time the review panel had ever met, or issued a decision, during the spy court's 25-year existence.
A key part of the review panel's ruling removed legal barriers between the surveillance operations of the Justice Department's criminal and intelligence divisions.
The decision "opens the door to surveillance abuses that seriously threatened our democracy in the past," justices were told in the filing by the ACLU, the National Association of Criminal Defense Lawyers, the American-Arab Anti-Discrimination Committee and the Arab Community Center for Economic and Social Services.
The Washington Post reports the TSA instructed local police on Feb. 8 to pull over drivers as they approach airport terminals for random searches of their vehicles.
The searches at all three major Washington area airports and across the nation have met resistance in some cities as airport managers assess their legality, the Post reports.
Some airport managers have refused to comply with the directive until the TSA clarified the legal issues. In its defense, the agency cited several cases in which federal courts ruled that vehicles could be searched for reasons of public safety.
"We have legal standing to do this and do it in a constitutional manner," TSA spokesman Robert Johnson told the Post. "Where there is a conflict, we'll work through that with local jurisdictions."
Constitutional experts said the TSA could face a fight over the new rules.
"There is a serious constitutional question about whether the federal government can direct local law enforcement agencies to do anything," Georgetown University law professor Mark Tushnet.
Important legal considerations include whether every driver will be stopped at a checkpoint or whether some will be selected at random, which potentially raises concerns about security officers improperly targeting drivers based on their race or religion, Barry Steinhardt, director of the ACLU's Technology and Liberty Project, told the Post.