Opponents of the program say the university is practicing illegal discrimination by considering race at all, especially since the school achieves significant diversity through its race-blind admissions.
No one on the court Wednesday expressed opposition to diversity in education. But Chief Justice John Roberts, Justice Antonin Scalia and Alito raised repeated objections to the affirmative action plan.
Roberts wanted to know how the university would determine when it had a "critical mass" of diversity on campus that would allow it to end the program.
Near the end of the session, he complained, "I'm hearing a lot about what it's not. I would like to know what it is."
Scalia, a dissenter in the 2003 case, mocked the university's efforts to have more minority students not just in the student body as a whole but at the classroom level.
"How do they figure out that particular classes don't have enough? What, somebody walks in the room and looks them over to see who looks Asian, who looks black, who looks Hispanic? Is that how it's done?" Scalia said.
After the argument concluded, Fisher read a brief statement outside in which she said she hoped the court would rule that race or ethnicity "should not be considered when applying to the University of Texas."
The university said in court papers that Fisher would not have been admitted even without a racial preference program.
The justices could sidestep the issue altogether. Texas argued that Fisher has no right to be in front of the court essentially because it can do nothing for her. She already has graduated from Louisiana State University, and the only money at issue in the case is her $100 application fee.
Justice Elena Kagan is not taking part, probably because she worked on the case at the Justice Department before joining the court.
A decision should come by late June.
Associated Press writer Jesse J. Holland contributed to this report.