With the future of public employee unions potentially at stake, the U.S. Supreme Court on Tuesday heard arguments in a case brought by Illinois homecare workers who object to fees charged by a union they don’t want to join.

During arguments in Harris v. Quinn, several justices—including, notably, Justice Antonin Scalia—said the case could drastically weaken unions that have long been allowed to charge nonmembers representation or agency fees to pay for collective bargaining that benefits all employees, including nonmembers.