The case is the latest installment in a decades-long campaign by prominent conservative foundations to weaken unions that represent public employees. They contend that requiring government workers to pay fees for collective bargaining and related activities violates the First Amendment.

“For too long, millions of workers across the nation have been forced to pay dues and fees into union coffers as a condition of working for their own government,” said Mark A. Mix, the president of the National Right to Work Legal Defense Foundation, which helped bring the new case. “Requiring public servants to subsidize union officials’ speech is incompatible with the First Amendment.”

The case concerns Mark Janus, who works for the state government in Illinois and is represented by the American Federation of State, County and Municipal Employees. He sued the union, saying he does not agree with its positions and should not be forced to pay so-called fair share fees to support its work.

The union’s president, Lee Saunders, said the case was an assault on the labor movement.

“The corporate C.E.O.s behind this case want to take away the freedom of working people to join together in a strong union and negotiate a fair return on their work,” Mr. Saunders said in a statement. “The rich and powerful interests behind this case are asking the Supreme Court to further rig the rules against working people and deny them the freedom to join together in a strong union to provide for their families, protect their communities and lift up the concerns of all working families.”