As usual, if the court takes on the dispute the main battle will be for the heart and mind of Justice Sandra Day O'Connor.
And, again as usual, the stakes are very high. Any decision in the case would affect colleges and universities across the country.
Actually, two University of Michigan cases have reached the Supreme Court. In one, a federal appeals court upheld the Law School's use of racial preferences in admissions policy to increase the number of minority students.
In the other, a federal judge upheld the use of racial preferences in the general admissions policy of the university as a whole. The challengers in the second case are asking the Supreme Court to review the dispute at once, despite the fact that an appeals court has not yet ruled on the matter.
The challengers in both cases are white applicants who were denied admission to the Law School or the university, but who would have been admitted had they been members of a racial minority.
The challengers cite the equal protection clause of the 14th Amendment -- equal protection under the law -- and Title VI of the 1964 Civil Rights Act, which bans discrimination based on "race, color or national origin."
The Supreme Court could decide whether it will review one or both of the cases before the New Year. If they do agree on review, the justices probably would hear argument in the spring.
A new and possibly bruising fight over affirmative action could not come at a worse time for the major political parties, both of which have put the issue on the back burner. Republicans are trying to make converts among racial-minority voters, especially in the growing Hispanic population. Democrats generally are trying to downplay liberal issues, such as affirmative action, which have caused working class and middle class whites to flee the party in droves.
But the Supreme Court is no respecter of politics, and the odds are that the justices will agree to hear at least one if not both of the Michigan cases -- it only takes four justices to vote to hear a case, and the principle at stake is important to both wings of the Supreme Court.
Over the last decade, the court's decisions on affirmative action usually have broken down along a 5-4 ideological fault line that has survived the retirement and replacement of several justices.
As it stands now, a majority made up of three reliable conservatives -- Chief Justice William Rehnquist and Justices Antonin Scalia and Clarence Thomas -- usually has been joined by the moderates, O'Connor and Justice Anthony Kennedy, to strike down government programs that are based on racial preference.
Though O'Connor is an integral part of this coalition, and very often writes its majority opinions, she has never taken the position that government programs based on race are always unconstitutional -- a position occasionally espoused in remarks from the bench by Scalia and Thomas.
Supreme Court opinions usually do not occur in isolation. Instead, they are built up gradually, precedent upon precedent, like multiple coats of paint on an old farmhouse wall.
O'Connor first came to the fore on the issue of affirmative action in 1993's Shaw vs. Reno. A slim majority headed by O'Connor struck down a new North Carolina congressional district because it was irregularly gerrymandered to achieve a black majority of voters.
Even as she attacked the race-based government action of redistricting, however, O'Connor left room for some programs to survive constitutional review.
"Classifications of citizens based solely on race are by their nature odious to a free people whose institutions are founded upon the doctrine of equality, because they threaten to stigmatize persons by reason of their membership in a racial group and to incite racial hostility," O'Connor said in the majority opinion in Shaw. "Thus, state legislation that expressly distinguishes among citizens on account of race -- whether it contains an explicit distinction or is 'unexplainable on grounds other than race' -- must be narrowly tailored to further a compelling governmental interest."
She went on to say that the Supreme Court "never has held that race-conscious state decision-making is impermissible in all circumstances."
O'Connor's views prevailed in a stream of other cases that struck down redistricting in other states because it was raced based.
In 1995's Adarand vs. Pena, a plurality led by O'Connor forced the Clinton administration to draw down its plans for an aggressive affirmative action plan.
But even as the Supreme Court struck down a government program giving preference to minority-owned businesses in U.S. Department of Transportation subcontracting, O'Connor conceded that race-based government programs could survive court scrutiny if they served "a compelling governmental interest" -- such as combating ongoing, rather than historical, racial discrimination.
The University of Michigan cases may ultimately turn on yet another Supreme Court precedent, one set before O'Connor was appointed as the court's first woman member in 1981 -- 1978's University of California Regents vs. Bakke.
In Bakke, a white applicant to the University of California Medical School at Davis was denied admission, even though less-qualified minority applicants were allowed to enroll.
Eventually, a 5-4 Supreme Court majority ruled that school admissions policies could take race into account, but they couldn't do so in a way that violated the Constitution's guarantee of equal protection for individual students.
Writing for the majority, Justice Lewis Powell said that racial and ethnic classifications by government "are inherently suspect and call for the most exacting judicial scrutiny."
While conceding that the "goal of achieving a diverse student body is sufficiently compelling to justify consideration of race in admissions decisions under some circumstances," he said that the California admissions policy, "which forecloses consideration to persons like (Alan Bakke), is unnecessary to the achievement of this compelling goal and therefore invalid under the equal protection clause."
The Supreme Court did three things in its decision: It ordered Bakke's admission. It struck down the California admissions policy. But it also, for the first time, said race-based admissions policies could be constitutional.
The University of Michigan, in briefs filed this week, told the Supreme Court that Bakke continues to be good law.
In asking that the justices not review the appeals court decision in its favor, the school said Bakke allows race to be one of the factors, if not the only factor, in an admissions policy.
How high are the stakes?
The school said a new Supreme Court decision overturning Bakke "would produce the immediate re-segregation of many -- and perhaps most -- of this nation's finest and most selective institutions."