In what could be a landmark case before the U.S. Supreme Court, the Justices hear arguments on Wednesday on a case involving affirmative action and college admissions, as the Court is being asked to invalidate race preferences used for some admissions by the University of Texas.

The case is being watched very closely because many believe there are already five votes on the High Court to do away with race based admission plans of any type.

Things were very different back in 2003, when the Court upheld an affirmative action plan in a case involving the University of Michigan; that decision was written by Justice Sandra Day O'Connor, but she is no longer on the bench.

"The recent changes in the Court's membership really do have the potential to make an outcome dispostive difference," said attorney Kannon Shanmugan at a recent Supreme Court symposium at the Cato Institute in Washington, D.C.

"I would agree; the handwriting is on the wall on the issue," added Tom Goldstein, who runs the scotusblog.com web site.

The basic thrust of this case involves a white woman named Abigail Fisher, who was rejected by the University of Texas in 2008; she argues that racial preference programs were part of that decision.

Some wonder if the Court will use this case to make a major statement - and overturn all racial preferences when it comes to college admissions, while others wonder if this will be an incremental change that tries to set a bright line for what colleges and universities can and cannot do.

Here is a video backing Fisher's argument produced by a group named the Project for Fair Representation.

There is one way though that the Supreme Court could sidestep this issue, at least for now - that's because Fisher has now graduated from Louisiana State University.

"The Court took this case fully aware of that," Goldstein said, raising the chance that "this case could turn into a nothing-burger" because Fisher has finished her undergraduate work.