In recent years, the nationwide Fight for $15 movement has succeeded in persuading several states and cities to raise their hourly minimum wages well above the federal minimum of $7.25.

But the effort to ensure a living wage for workers may be headed for a serious setback in the U.S. Supreme Court.

Depending on how they rule in a case set for argument next week, the justices could make it much more difficult for millions of workers to secure even the meager wages guaranteed by existing federal law.

On Monday, the day that kicks off the Supreme Court’s new term, the justices will hear arguments in three consolidated cases with far-reaching implications for wage-earners.

The cases—Epic Systems Corp. v. Lewis, Ernst & Young LLP v. Morris, and National Labor Relations Board v. Murphy Oil USA, Inc.—are all about whether employers have the right to compel workers go through onerous individual arbitration proceedings in order to bring labor law claims. If the justices answer that question in the affirmative, then the affected workers will—as a practical matter—find it nearly impossible to win back pay in cases involving wage law violations.

In the typical case involving wage law violations—such as when a firm makes employees work off the clock, pays less than the minimum wage, or fails to pay extra for overtime—plaintiffs bring what’s called a collective action (similar, but not identical to, a class action) in order to recover back pay from a common employer.

Each worker’s claim might be worth only a few hundred or few thousand dollars, but when the defendant is a large firm with lots of similarly situated employees, the collective action might be worth millions. So while virtually no lawyer would want to take on an individual case on behalf of such a plaintiff, it’s much easier to find competent counsel to litigate a potentially more lucrative collective action.

To pre-empt this possibility, more and more firms are inserting individual arbitration clauses into employee contracts. These clauses require employees to pursue workplace-related claims before private arbitrators rather than in federal or state court. These clauses also, critically, require employees to pursue their claims individually rather than through collective actions.

In 2012, the National Labor Relations Board sought to stop this trend, along with its potentially devastating consequences for workers seeking legally mandated compensation. It ruled that individual arbitration clauses violate the National Labor Relations Act of 1935, also known as the Wagner Act.

The Wagner Act makes it illegal for an employer to “interfere with, restrain, or coerce employees in the exercise” of their right “to engage in ... concerted activities for the purpose of ... mutual aid or protection.”

The board’s interpretation that individual arbitration clauses violate the Wagner Act follows straightforwardly from the language of the act itself and the cases construing it. The Supreme Court has said that the act encompasses efforts by employees to come together to use administrative and judicial proceedings to protect these rights.

Additionally, a well-entrenched rule of administrative law holds that courts should defer to a federal agency’s reasonable interpretation of the statute that it administers, and that rule ought to apply to the board’s interpretations of the Wagner Act.

Employers, however, have pushed back against the NLRB’s ruling. They argue that a 1925 law, the Federal Arbitration Act, requires courts to enforce the individual arbitration provisions as written.

That statute says that a “written provision in … a contract ... involving commerce to settle by arbitration a controversy … shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law.” In other words: An arbitration clause is enforceable unless some other legal source says that it’s not.

The employers’ argument should fail for two reasons. First, the NLRB’s 2012 ruling actually allows employers to insert collective arbitration clauses into employment contracts.

On this view, there is no conflict between the Federal Arbitration Act and the Wagner Act. There is only a conflict between the Wagner Act and provisions of employment contracts that prevent workers from exercising their rights in concert.

Second, even if the Federal Arbitration Act and the Wagner Act clash, it’s the Wagner Act that should take precedence. This is because the Federal Arbitration Act clearly says that it will yield to another federal law that conflicts. Recall that the 1925 law provides that arbitration clauses are enforceable “save upon such grounds as exist at law.” So the tie goes to the Wagner Act.

Consistent with this last argument, the 7thand 9th U.S. Circuit Courts of Appeals have both held that individual arbitration provisions in employment contracts are unenforceable. But several other courtshave sided with the employers. Meanwhile, the Justice Department, which initially defended the board’s position, switched sides this past June.

In recent years, the Supreme Court has used the Federal Arbitration Act to compel the enforcement of arbitration clauses in cases where the drafters of the statute never would have expected it to apply. If current trends continue, then the Wagner Act will be the next casualty as the court’s conservative majority beats a pro-arbitration path.

A ruling for the employers would not mean an outright end to the enforcement of minimum wage and overtime laws. The Department of Labor and state agencies still would have authority to pursue wage law violators. Some employers still would refrain from inserting individual arbitration clauses into contracts, and perhaps a few plucky employees who are subject to such clauses would bring individual claims on their own.

But according to the most recent data, workers won $467 million in class and collective actions alleging wage law violations in 2013—more than was recovered by federal and state officials in enforcement actions. If the justices side with the employers here, look for that figure to drop precipitously and for many more workers to be denied their legally earned wages.

Ultimately, cities and states at the forefront of the fight to expand worker protections will be left with limited options. They can’t override the Federal Arbitration Act, because of the Constitution’s Supremacy Clause.

They can step up their own efforts to go after violators, but they will largely lose the ability to rely on private plaintiffs’ attorneys to aid in the enforcement of wage laws. Their best hope is that the Supreme Court will finally put a halt to what seems like its limitless expansion of arbitration provisions in recent cases.

Otherwise, the Fight for $7.25 may soon become a much tougher battle.