The case for now is the largest class action in U.S. history, but the five-member conservative majority on the nine-member high court may derail it, judging by comments from the bench during argument.
Justice Anthony Kennedy, a key swing vote who normally helps form the five-member conservative majority, said, "It's not clear to me: What is the unlawful policy that Walmart has adopted, under your theory of the case?," SCOTUSBLOG.com reported.
Plaintiffs attorney Joseph Sellers said Walmart store managers have been given "unchecked discretion," and they use it to discriminate against women.
Kennedy said the complaint "faces in two directions. ... You said this is a culture where ... the company headquarters knows everything that's going on. Then ... you say ... these supervisors have too much discretion. It seems to me there's an inconsistency there, and I'm just not sure what the unlawful policy is."
Kennedy was seconded by fellow conservative Justice Antonin Scalia.
CNN also reported the female workers were facing an uphill battle, saying the narrow conservative majority appeared skeptical about allowing workers from across the country to file one suit and undergo one trial.
The court's three female members -- liberal Justices Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan -- appeared to favor the plaintiffs, CNN said.
The Supreme Court is not reviewing the merits of the suit -- whether Walmart is guilty of discrimination against women -- but whether the enormous class action, with a possible 1.5 million plaintiffs, should be allowed to proceed.
The case started in San Francisco in 2001 when six women filed suit claiming discrimination, in part because they were passed over for promotion in favor of men. One says she was told, "It's a man's world."
"This nationwide class includes every woman employed for any period of time over the past decade, in any of Walmart's approximately 3,400 separately managed stores, 41 regions and 400 districts, and who held positions in any of approximately 53 departments and 170 different job classifications," the company's petition to the Supreme Court said. "The millions of class members collectively seek billions of dollars in monetary relief under Title VII of the Civil Rights Act of 1964, claiming that tens of thousands of Walmart managers inflicted monetary injury on each and every individual class member in the same manner by intentionally discriminating against them because of their sex, in violation of the company's express anti-discrimination policy."
The petition questions whether monetary claims can be brought under Rule 23 of the Federal Rules of Civil Procedure "which by its terms is limited to injunctive or corresponding declaratory relief."
A federal appeals court panel and the full U.S. Court of Appeals for the 9th Circuit, both divided, approved the certification of the class.
The Supreme Court should hand down a decision before the summer recess in late June or early July.