Former Justice Sandra Day O’Connor famously imposed an expiration date on affirmative action, writing in the 2003 majority ruling that she expected race-based preferences would no longer be needed to balance out school admissions in 25 years.

The Supreme Court will take up her challenge Monday with the clock ticking toward her deadline.

Two cases — one challenging Harvard University, the other the University of North Carolina at Chapel Hill — give the justices their best chance in decades to deliver a firm set of rules to schools still struggling with thorny issues of race and whether the Constitution requires colorblind treatment or allows for proactive discrimination in favor of minorities.

The Asian American plaintiffs upend the usual debate and add a layer of nuance to what has been a largely Black and White issue.

Devon Westhill, president and general counsel of the conservative think tank Center for Equal Opportunity, said he figures the justices will take O’Connor’s challenge to heart and tell schools that admissions decisions cannot rely on race.

“I expect the court will go as far as doing that. It’s been meddling in racial preference cases, particularly higher education cases, for 40-some-odd years, but I think the current ‘conservative’ majority is prepared to right some precedential wrongs,” Mr. Westhill said.

Those precedents stretch back to 1978’s Bakke case out of California, in which the high court allowed race to be considered in admissions but ruled against strict quotas; a pair of cases out of Michigan in 2003 that said race could be considered a “plus” factor, but no more; and a 2016 decision out of Texas that largely reaffirmed the Michigan rulings.

It was in one of the cases in 2003 — Grutter v. Bollinger — that O’Connor, the swing vote in the pair of 5-4 rulings, offered her timeline: “The Court expects that 25 years from now, the use of racial preferences will no longer be necessary to further the interest approved today.”

The statement was startling. Constitutional rights don’t usually come with expiration dates.

Justice Clarence Thomas, who was on the court in 2003 and is still serving, agreed that racial preferences would be illegal in 25 years, but he said they should have been illegal in 2003, too.

All eight other members of the current court joined after that decision, though Chief Justice John G. Roberts Jr. and Justices Samuel A. Alito Jr. and Sonia Sotomayor were part of the 2016 ruling.

How much O’Connor’s 25-year timeline weighs on the court is impossible to say.

Opponents of racial preferences occasionally cited O’Connor’s words in their briefs, while supporters of using race usually did not.

Both sides agree that the problems confronting O’Connor remain as the country nears the 25-year mark.

Mr. Westhill said that’s a reason to move beyond the racial preferences experiment.

“I think we’ve gone to a place that is the antithesis of what she predicted,” Mr. Westhill said. “What we see now is much less racial harmony and much more racial strife and division, in part due to the mess the Grutter court created.”

David H. Gans, director of the Human Rights, Civil Rights & Citizenship Program at the liberal Constitutional Accountability Center, said the persistent difficulties are the reason to stay the course.

“And, as a number of briefs before the court explain, because of continuing racial inequality in educational opportunity, race-conscious admissions continue to be necessary to ensure a diverse student body and provide pathways to leadership to qualified persons of all races,” Mr. Gans said.

He said O’Connor’s 25-year timeline was what is known as “dicta,” offering insight into a judge’s thinking but not binding other courts.

Mr. Gans said the real issue before the justices is whether the equal protection clause of the 14th Amendment is a shield, blocking the use of race as a consideration, or whether it’s a sword to be wielded on behalf of oppressed minorities “to foster equality.”

“Indeed, the framers of the Fourteenth Amendment were the originators of affirmative action and race-consciousness is baked into the text and history of the Fourteenth Amendment,” Mr. Gans said in an email.

That debate over the intent of the 14th Amendment has raged in the briefs filed with the high court.

Some scholars conclude that the framers wanted a race-blind approach. Others say the framers envisioned proactive steps by the government to equalize races — or what we now call affirmative action.

The Asian angle adds a new wrinkle.

From Allan Bakke’s case in 1978 to the plaintiffs in the two Michigan cases to Abigail Fisher in the 2016 Texas case, every major affirmative action admissions test to reach the justices has involved a White plaintiff.

Students for Fair Admissions, the plaintiff at the heart of the North Carolina and Harvard cases, sought out Asian Americans to argue that promoting the interests of Black and Hispanic students harms another minority.

That raises questions about whether the 14th Amendment’s equal protection clause is aimed chiefly at Blacks or whether it covers a broader sense of minorities.

At Harvard, for example, an Asian man with a 25% chance of admission based on his credentials would have a 36% chance of admission if he were White, a 75% chance of admission if he were Hispanic and 95% if he were Black, according to calculations by Duke University economics professor Peter Arcidiacono.

Mr. Gans said he doesn’t think Asian American plaintiffs will make much of a difference.

He said the arguments before the justices don’t delve into the Asian aspect in any substantial way. Instead, he said, the case goes to the heart of the big questions about race.

“SFFA’s main submission is that the Constitution requires absolute colorblindness and that the use of race to achieve a diverse student body is no different than Jim Crow segregation struck down in Brown v. Board of Education,” he said. “Given that, I don’t expect the identity of the plaintiff to figure heavily.”

Mr. Westhill said he also expects the court to take up the deep issues of race and the equal protection clause. If the majority of justices don’t want to go that far, he said, the Asian aspect does offer an off-ramp to rule against Harvard’s policy without delivering a new standard for all schools.

Whatever the legal angles, the Asian plaintiffs reframe the debate for the public.

“The narrative in the United States — and it’s true — is that Black and Brown people have been oppressed for long periods of our history, if not still today, and white people maybe had it coming,” Mr. Westhill said. “Now we see this script flipped on its head.”

Mr. Westhill said he is figuring on a 6-2 decision against Harvard’s use of race, with all six Republican-appointed justices in the majority. He also said Chief Justice Roberts, despite past rulings decidedly opposed to race-based preferences, could dissent with an eye to other issues surrounding the court’s public standing.

Justice Ketanji Brown Jackson, new to the Supreme Court, is recused from the Harvard case, though she will participate in the North Carolina case.