The Grutter decision allowed but did not require states to take account of race in admissions. Several states, including California and Michigan, forbid the practice, and public universities in those states have seen a drop in minority admissions. In other states and at private institutions, officials generally look to race and ethnicity as one factor among many, leading to the admission of significantly more black and Hispanic students than basing the decisions strictly on test scores and grades would.

A Supreme Court decision forbidding the use of race in admission at public universities would almost certainly mean that it would be barred at most private ones as well under Title VI of the Civil Rights Act of 1964, which forbids racial discrimination in programs that receive federal money. In her majority opinion in Grutter, Justice O’Connor said the day would come when “the use of racial preferences will no longer be necessary” in admission decisions to foster educational diversity. She said she expected that day to arrive in 25 years, or in 2028. Tuesday’s decision to revisit the issue suggests the deadline may arrive just a decade after Grutter.

The court’s membership has changed since 2003, most notably with the appointment of Justice Samuel A. Alito Jr., who replaced Justice O’Connor in 2006. Justice Alito has voted with the court’s more conservative justices in decisions hostile to government use of racial classification.

Chief Justice John G. Roberts Jr. has been particularly skeptical of government programs that take account of race. “Racial balancing is not transformed from ‘patently unconstitutional’ to a compelling state interest simply by relabeling it ‘racial diversity,’ ” he wrote in a 2007 decision limiting the use of race to achieve integration in public school districts.

Justices Alito, Antonin Scalia and Clarence Thomas agreed. Justice Anthony M. Kennedy, the court’s swing justice, also voted to invalidate the programs. But he was less categorical, sharply limiting the role race could play in children’s school assignments but stopping short of forbidding school districts from ever taking account of race. Still, Justice Kennedy has never voted to uphold an affirmative action program.

In Texas, students in the top 10 percent of high schools are automatically admitted to the public university system, a policy that does not consider race but increases racial diversity in part because so many high schools are racially homogenous. Ms. Fisher just missed that cutoff at her high school in Sugar Land, Tex., and then entered a separate pool of applicants who can be admitted through a complicated system in which race plays an unquantified but significant role. She sued in 2008.