Like the retail behemoth at its center, everything about the Supreme Court extravaganza known as Wal-Mart v. Dukes is super-sized.

The number of women who could be included in the sex discrimination class-action suit is measured in millions. The amount of damages for which the nation’s largest private employer could be liable is estimated in billions.

If the Supreme Court agrees the case can move forward, it would be the largest employment discrimination class-action suit in U.S. history. As Wal-Mart likes to point out, the suit could include more people than the number now serving in the Army, Navy, Air Force, Marines and Coast Guard combined. Oral arguments are scheduled for Tuesday.

The prospect of such a massive lawsuit — or, alternatively, a ruling that hobbles workers from mounting class-action suits against large, national employers — has drawn an outpouring of competing briefs from corporate America and the nation’s leading civil rights groups.

The suit, filed by six female Wal-Mart employees in 2001, will also spotlight two intriguing story lines about the Supreme Court.

One is the perception, reinforced by President Obama, congressional Democrats and civil rights groups, that the court is overly protective of the corporate world. There is evidence to support the claim as well as exceptions, but there seems little doubt about how a ruling for Wal-Mart would be portrayed by liberal groups already suspicious of the court and the huge company.

Also notable is that the case — featuring charges by women of unequal pay, sexist remarks and insurmountable obstacles to promotion — arrives at a court whose membership for the first time is one-third female.

Justice Ruth Bader Ginsburg, 78, the oldest member of the court, made her career advancing the rights of women and challenging laws that treated the sexes differently. She has been joined by fellow Democratic nominees Sonia Sotomayor and Elena Kagan.

“The mere presence of three female justices on a previously male-dominated bench gives the plaintiffs’ side a symbolic boost,” said Barbara Perry, who studies the court at the University of Virginia’s Miller Center for Public Affairs. Referring to the Wal-Mart greeter who is the lead plaintiff in the case, she added, “The more women on the bench, the more likely Betty Dukes’ story of discrimination will resonate.”

That said, Perry also noted that the court is not deciding whether Wal-Mart is guilty of discrimination. Instead, it will decide whether the small group of plaintiffs have satisfied federal class-action rules, allowing them to stand for co-workers nationwide who they say have suffered under common discriminatory practices. The class would include all women who have worked at Wal-Mart since December 1998.

A federal judge in San Francisco ruled that the suit could go forward. The plaintiffs’ attorney, Brad Seligman, a class-action specialist at the Impact Fund, a tiny public-interest law firm in Berkeley, Calif., assembled statistics showing that women constitute 80 percent of hourly Wal-Mart workers but hold only a third of managerial jobs. The percentage decreases on each step up the company hierarchy.

There were allegations of pay disparities between men and women; a lack of job postings, keeping women from career advancement; and a generally hostile work environment for women. Affidavits from more than 100 female workers brought stories of women being called “Janey Qs” and being told that men were paid more because they had families to support, as well as a worker’s complaint that her male manager told her to “doll up.”

Seligman said that although pay and promotion decisions are made at the local level, they reflect an attitude from the top.

“Wal-Mart has a very in-depth training program, very careful corporate oversight, a strong corporate culture, all designed to ensure a uniformity in decision making,” he said in a recent interview.

Wal-Mart responds in its brief to the court that because the plaintiffs cannot prove the company has a doctrine of discrimination — indeed, it has a specific policy of nondiscrimination — “plaintiffs premised their motion on statistics, sociology, and anecdotes.”

At the time of the district judge’s decision in 2004, the company’s retail operation included seven divisions, 41 regions, 3,400 stores and more than 1 million employees.

“The named plaintiffs’ claims cannot conceivably be typical of the claims of the strangers they seek to represent,” Wal-Mart said.

The case languished for years at the U.S. Court of Appeals for the 9th Circuit in San Francisco before a panel upheld the judge’s decision. The full court agreed in a 6 to 5 decision, although the dissenters practically urged the Supreme Court to take up the issue.

The millions of women who have worked at Wal-Mart, Circuit Chief Judge Alex Kozinski wrote, “have little in common but their sex and this lawsuit.”

The company contends that the plaintiffs’ goals of back pay, punitive damages and a change in the company’s allegedly discriminatory practices run counter to the court’s past decisions on class certification.

Wal-Mart’s attorney in the case, Los Angeles lawyer Theodore J. Boutrous Jr., said the company is not arguing that the size of the potential class — which Seligman estimates would be at least 1 million women — renders it unworthy of certification.

“But the size of the class does really magnify the deeper problems of the case,” he said in an interview. Seligman said a class-action suit is the only way to help women who have encountered discrimination. The average difference in annual pay between male and female workers, he said, was a little more than $1,000.

“These are not cases they could possibly find counsel to litigate, even if they were willing to go up against Wal-Mart,” he said.

Civil rights and public-interest groups say the case is important because of the message it would send about the avenues available to employees at big companies. Paul Bland, a senior lawyer at Public Justice, said Wal-Mart is pushing a message that it is “too big to sue.”

By agreeing, he said, the justices would be saying, “As long as you discriminate against enough people, courts can’t get involved.”

But Robin Conrad of the U.S. Chamber of Commerce said a decision upholding the plaintiffs would turn even frivolous class-action suits into “bet-the-company propositions” for employers who would not want to risk the potential losses at trial.

“If this class action gets certified, it’s open season for all class actions to be certified,” not just for discrimination claims but also for product liability and financial services, she said.