Protecting Our Supreme Court Justices Act of 2023 This bill enhances the prison term for an individual who pickets or parades in or near a U.S. court or a judge's residence with the intent of (1) interfering with, obstructing, or impeding the administration of justice; or (2) influencing a judge, juror, witness, or court officer. Specifically, the bill increases the maximum prison term from one to five years.