WASHINGTON — U.S. Supreme Court justices voiced strong doubts Tuesday about allowing students or their parents to sue local school districts for failing to prevent sexual harassment by their classmates.

“I’m sure schoolchildren nationwide tease each other. Little boys tease little girls,” Justice Sandra Day O’Connor said firmly at the start of arguments in a Georgia case, Davis v. Monroe County Board of Education , 97-843. “Is every one of those incidents going to lead to a lawsuit?”