In a California case to be argued Monday, the U.S. Supreme Court appears poised to strike a devastating blow against government employee unions by stripping them of their power to charge fees to nonmembers for the costs of representing them at the bargaining table.

The unions’ best hope of averting disaster would seem to be, of all people, Justice Antonin Scalia.

At issue in Friedrichs vs. California Teachers Association is the relationship between public employee unions, such as the 325,000-member CTA, and the minority of workers who have chosen not to become members.

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“The viability of public-sector unions is at stake,” said William Gould, a Stanford law professor, chairman of the state farm labor board and former chairman of the National Labor Relations Board.

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A ruling eliminating fees for nonmembers would be “directly at odds with where Scalia was going” in his 1991 opinion, said Stanford’s Gould, one of a group of labor law professors who filed arguments with the court supporting the unions. He acknowledged, however, that the odds are against them.