At the same time, the court will decide for the first time whether to extend equal rights to gay couples who are married and to gays and lesbians who wish to marry.
In both sets of cases, the justices will consider what the Constitution means when it says the government may not deny to any person "the equal protection of the laws."
That simple command drove the decisions that struck down racial segregation, integrated classrooms and colleges, and encouraged the adoption of affirmative action policies. And the Voting Rights Act finally gave blacks an equal right to cast ballots and to elect their favored candidates across the South.
More recently, however, conservatives have pushed back, arguing that race-based policies are suspect and discriminatory, even if their aim is to benefit racial minorities. And Chief Justice John G. Roberts Jr. has said the Voting Rights Act is less about voting these days and more about what he called the "sordid business [of] divvying us up by race" when drawing electoral districts.
Meanwhile, gay rights advocates have been sounding the call for equality before the law. They have been winning in state courts, state legislatures, at the ballot box and in polls of public opinion. Twelve states now authorize same-sex marriage, twice as many as last year. But they have yet to win a true declaration of equal rights under the Constitution.
That could come soon. The court will decide whether to strike down the Defense of Marriage Act and rule that legally married gay couples deserve equal benefits under federal law. The California case on Proposition 8 asks the court to decide whether gays and lesbians have an equal right to marry under the Constitution.
Both sets of cases on racial equality and gay rights are linked thematically, says Erwin Chemerinsky, dean of the University of California, Irvine Law School.
"I do think there is a parallel. I think the Court can regard DOMA and Prop. 8 as the type of blatantly discriminatory laws that were struck down in the race area decades ago," he said. "But affirmative action and Section 5 [of the Voting Rights Act] are different in the view of the conservative majority: they are remedies that are no longer needed."
The cases also offer the justices the choice to rule broadly or narrowly. Because they are closely divided on these issues, they could be in search of narrow options that win over a majority.
For example, the University of Texas case could lead to a nationwide ruling that strikes down race-based college admissions policies, or it could yield a narrow, Texas-only ruling.
Thanks to a state measure known as the Top 10 percent law, the Austin campus has seen a steady influx in Latino students and a slight rise in the percentage of black students. These minority students were admitted because they graduated in the top 10 percent of their high school classes, not because they were given a preference through the affirmative action policy. Because this policy has been so successful in bringing racial and ethnic diversity to the campus, the Supreme Court could rule that a race-based admissions policy is no longer needed or justified in this instance.
Last year, when the court voted to hear a white student's challenge to the University of Texas, many on the right hoped for a broad ruling to void race-based policies. The case was argued in October. The long delay in handing down an opinion has now led many to suspect the outcome will mean much less.
Four years ago, the court under Roberts came close to striking down Section 5 of the Voting Rights Act, but stopped short. Even some of the court's conservatives, though skeptical, were unwilling to sign their names to an opinion that voided one of the nation's most effective civil rights laws, and one that Congress had just extended on a near-unanimous vote. This year, defenders of the law hope the court will stop short again.
Like the Texas case, the California case on same-sex marriage could lead to a nationwide ruling, or more likely, a California-only decision.
Justice Anthony M. Kennedy and the court's four liberal justices are expected to join to strike down the federal Defense of Marriage Act. Such a ruling would benefit more than 100,000 married gays and lesbians.
But Kennedy and Justice Ruth Bader Ginsburg have been wary of going too far too fast when society is changing. A veteran of the women's rights movement, Ginsburg has repeatedly said she believes in a step-by-step approach toward full equality, rather than a single national ruling by the Supreme Court.
If so, the justices could decide the fate of Prop. 8 in a way that does not force the other 37 states to immediately change their marriage laws.
Then, with popular support for gay marriage steadily rising, they may wait to see how the issue develops before revisiting it.