By the conclusion of the argument, it seemed tolerably clear that the four members of the court’s conservative wing were ready to act now to revise the Grutter decision.

The court’s more liberal members said there was no reason to abandon the earlier framework. “What is it we’re going to say here that wasn’t already said in Grutter?” Justice Breyer asked.

Justice Elena Kagan disqualified herself from the case, Fisher v. Texas No. 11-345, presumably because she had worked on the case as solicitor general. That leaves open the possibility of a 4-to-4 tie, which would have the effect of affirming a lower-court decision upholding the Texas program.

Ms. Fisher, 22, recently graduated from Louisiana State University and works as a financial analyst in Austin, Tex. Her lawyer, Bert W. Rein, was questioned closely by the more liberal justices about whether she suffered the sort of injury that gives her standing to sue.

They also pressed the point that the Texas program should pass muster under the 2003 decision. “It seems to me that this program is no more aggressive than the one in Grutter,” Justice Ruth Bader Ginsburg said. “In fact, it’s more modest.”

Three-quarters of applicants from Texas are admitted to the university under a program that guarantees admission to the top students in every high school in the state. That program, which has produced substantial diversity, is not directly at issue in the case.

Students from Texas who missed the cutoff, like Ms. Fisher, and those from elsewhere are considered under standards that take account of academic achievement and other factors, including race and ethnicity.