WASHINGTON - The future of affirmative action at public universities appeared in some doubt Wednesday as the Supreme Court debated for a second time whether to strike down a race-based admissions policy at the University of Texas.

It was clear the court's conservatives, including Chief Justice John G. Roberts Jr., believe using affirmative action in admission decisions is unconstitutional.

When a university lawyer spoke of the importance of classroom diversity, Roberts asked: "What unique perspective does a minority student bring to a physics class?"

In the past, when the high court has upheld affirmative action, it did so with the understanding that it was a temporary measure, Roberts said. "When do you think your program will be done?" he asked.

The liberals, led by Justice Sonia Sotomayor, spent much of the hour arguing in defense of the university's policy in Fisher v University of Texas. The federal appeals court in New Orleans has twice upheld the Texas admissions program.

Sotomayor, the court's first Latina, grew up in the Bronx and said she had benefited from affirmative action when she was admitted to Princeton University.

"I fear something. I do have a worry" that the court is on the verge of shutting down affirmative action at state universities across the nation, she said.

By contrast, Justice Antonin Scalia questioned whether affirmative action truly benefited black students.

"There are some who contend it does not benefit African Americans to get them into the University of Texas, where they do not do well, as opposed to having them go to a less advanced school, a slower-track school, where they do well," Scalia said.

He was referring to the "mismatch theory" originally set out by University of California, Los Angeles law professor Richard Sander, which contends black students sometimes fare badly if they are admitted to a top-tier law school. The students would have done better had they enrolled in another law school that was somewhat less demanding, the theory holds.

Scalia said he was not convinced the University of Texas needed more black students. "Maybe it ought to have fewer," he said. "I don't think it stands to reason that it's a good thing for the University of Texas to admit as many blacks as possible."

Justice Anthony M. Kennedy, who almost surely holds the deciding vote, voiced frustration because university lawyers could not quantify in detail what role race plays in Texas in determining which students are admitted.

"We're just arguing the same case again," he said at one point, referring to the fact that the court had heard the same case two years ago and sent it back to a lower court for review. The case began when Abigail Fisher, a white applicant, filed suit after she was turned down for admission in 2008. She has since graduated from Louisiana State University.

Because the White House filed an early brief on the university's side when Elena Kagan was solicitor general, now-Justice Kagan sat out the case. If Kennedy votes with the three liberals, the court will be split 4-4, which would affirm the lower court's ruling backing the admissions policy.