WASHINGTON — The massive class action against retail giant Wal-Mart Stores Inc. ran into stiff resistance at the U.S. Supreme Court today, after surviving lower court challenges ever since it was launched 10 years ago.

“It’s not clear to me: What is the unlawful policy that Wal-Mart has adopted?” said Justice Anthony Kennedy, who as usual is the likely swing vote in the closely watched business case Wal-Mart v. Dukes. The outcome of the dispute, involving as many as 3 million female current and former workers, could cost Wal-Mart billions in back pay or limit the use of class actions as a civil rights remedy.