WASHINGTON — In a case that could affect the education of 6.7 million children with disabilities, the Supreme Court on Wednesday struggled to decide whether it should require public schools to do more under a federal law that calls for them to provide a free education that addresses the children’s needs.

Justice Samuel A. Alito Jr. said the court was being asked to choose among several finely shaded formulations. “What is frustrating about this case and about this statute is that we have a blizzard of words,” he said.

The court appeared uneasy with a standard used by many appeals courts, which have said that providing a modest educational benefit was enough. But some of the justices indicated that they were concerned about the costs that any changes could impose.

Justice Stephen G. Breyer said that a new standard might also invite costly litigation. “If we suddenly adopt a new standard, all over the country we’ll have judges and lawyers and people interpreting it differently,” he said. “I foresee taking the money that ought to go to the children and spending it on lawsuits and lawyers and all kinds of things that are extraneous.”