Lawprof Rick Hasen (Election Law blog) predicts a 9-0 vote upholding the law, and reversing the Washington Supreme Court's decision holding that the law violated the union's First Amendment rights. I cowrote an amicus brief in the case on that side, and I'm pleased to hear Rick's prediction. It's generally risky to put much stock on prediction from oral arguments, but here the case in favor of the law's constitutionality strikes me as objectively very strong (for the reasons mentioned in the brief), and the oral argument analysis thus strikes me as especially plausible.

UPDATE: Lawprof Paul Secunda (Workplace Prof blog) agrees that this is the likely result, though by a 7-2 vote.