WASHINGTON — The Supreme Court on Wednesday seemed poised to rule that states may not exclude religious schools from state programs that provide scholarships to students attending private schools.

Chief Justice John G. Roberts Jr., looking none the worse for wear after a late night presiding over the impeachment trial of President Trump, seemed to be searching for a limiting principle, one that would allow the scholarships but stop short of requiring state support for religious education in other contexts.

“I wonder,” the chief justice said, “if there’s a difference between general funding of the public schools and the decision to provide aid to private schools, except not religious schools.”

Justice Stephen G. Breyer, a member of the court’s liberal wing, asked questions along the same lines.