The use of racial preferences in university admissions appears to be in jeopardy — at least at the University of Texas, if not nationwide.

With the author of the last landmark affirmative action case, retired justice Sandra Day O’Connor, seated in the front row, the Supreme Court openly struggled Wednesday with this central question: How much racial favoritism is enough?

Programs used by university admissions offices nationwide to achieve diversity hung in the balance as the court took up the case of Fisher v. University of Texas, the latest in a long string of affirmative action cases that until now have upheld the limited use of race in college admissions.

As the justices peppered questions at lawyers for the university and for Abigail Fisher, the 22-year-old Texan who says she was denied admission to the school’s flagship campus in Austin because she was white, it became clear they were searching for a bright line that does not exist.