CHESTER, Ill. — Randy Clover is something of an anomaly — the president of a union local here that represents Illinois state employees, and a Republican precinct leader who voted for President Trump. But he has no doubt about what will be at stake next week at the Supreme Court: the financial and political clout of one of organized labor’s last strongholds.

The court will hear arguments on Monday about whether the government employees represented by Mr. Clover’s union, the American Federation of State, County and Municipal Employees, must pay the union a fee for representing them in collective bargaining. Conservative groups, supported by the Trump administration, say the First Amendment bars forcing government workers from having to pay anything, and the court has sent strong signals that it agrees with that argument.

If it does, unions like Mr. Clover’s stand to lose fees not only from workers who object to the positions they take in negotiations but also from anyone who chooses not to join a union but benefits from its efforts. To hear Mr. Clover tell it, the case is the culmination of a decades-long assault against the labor movement.

“The case was started by the governor to destroy unions,” Mr. Clover said, referring to Gov. Bruce Rauner, a Republican who has been at war with Illinois’s public-sector unions. “It’s trying to diminish the protections that unions have for their members.”