WASHINGTON, Aug. 3 -- As the Supreme Court's calendar turns from the frantic final days of June to the fresh beginning of the first Monday in October, Sandra Day O'Connor is once again the Justice on the spot.

Throughout her 16-year tenure, Justice O'Connor has been at the center of many of the Court's most polarizing and important debates, whether the subject was abortion, religion or, as in the last term, federalism.

Now the subject is race, and in no area has Justice O'Connor played such a vital role over so many years as in the Court's struggle over whether, and to what purpose, the Government may ever take race into account.

Whether the context has been the role of race in electoral politics or the validity of set-aside programs to steer Government business to minority contractors, she has typically either written the opinions or cast the deciding vote in 5-to-4 decisions to treat race-conscious Government policies as highly suspect.

''O'Connor has rejected both of the ideologically pure positions about race-conscious public policy, one being that anything that overcomes the disadvantage of race is good, and the other that taking race into account is never appropriate,'' Prof. Richard H. Pildes of the University of Michigan Law School said in an interview. ''She has been groping for an intermediate, subtle, fine-grained position.''

Now for the first time in a decade, the Justices are about to take up the highly charged question of affirmative action, more often portrayed as a zero-sum game than an occasion for subtle line-drawing. People who agree on little else about the subject are united in the belief that the future of affirmative action may well be in Justice O'Connor's hands.

On the last day of the term, the Court announced it would hear an affirmative action case from a New Jersey school district, where officials dismissed a white teacher in order to preserve a black teacher's job. Overshadowed by the headline-grabbing flood of opinions in the term's final days, the Court's action has so far received relatively little public notice.

That is about to change. Just as the last Supreme Court term provided a stage for a searching public inquiry into physician-assisted suicide, the case of Piscataway Board of Education v. Taxman will most likely be the centerpiece of the new term, doing more to galvanize debate over affirmative action than any Presidential speeches or commissions.

The grant of review hardly went unnoticed by stakeholders in the affirmative action debate. In the six years since the Bush Administration went to court on behalf of Sharon Taxman, the dismissed white teacher -- a position the Clinton Administration later disavowed -- the Piscataway case has been a mirror of the shifting political currents on the subject of race.

Advocates on both sides have watched the twists and turns of a case that in many respects appears to put affirmative action in the worst possible light. A race-based layoff is a harder sell, both politically and legally, than almost any other race-conscious policy.

So the news that this case would be the Supreme Court's vehicle for revisiting affirmative action was greeted with either glee or dread by those who have viewed this case as either an opportunity or a train wreck. Groups on both sides are working on their briefs, no doubt tailored to win Justice O'Connor's attention and vote.

There is a parallel: almost exactly 20 years ago, the case of Allan Bakke, a white man whose effort to gain entrance to a California state medical school was frustrated by a policy that set aside a fixed number of places for minorities, set off a furious public debate. Justice O'Connor had not yet joined the Court, but there was another Justice in the middle, Lewis F. Powell Jr., now retired. Like Justice O'Connor, he was a moderate conservative with an aversion to the absolutist views on both ends of the spectrum.

With the Court otherwise split 4 to 4, Justice Powell's separate opinion defined the Court's position. The Bakke decision repudiated quotas but kept affirmative action alive by endorsing the goal of student diversity in higher education as a compelling governmental interest. Until last year's Hopwood decision, in which a Federal appeals court invalidated the affirmative-action admissions program at the University of Texas Law School in a ruling the Supreme Court declined to review, the Bakke case remained the law of the land. The underlying question in the new case is whether it still is.

''For better or worse, this is the vehicle for settling the diversity question,'' said Clint Bolick, president of the Institute for Justice, a conservative public interest law firm here that opposes affirmative action. ''O'Connor is pivotal on both the direction and distance the Court will travel.''

Would Justice O'Connor have voted as Justice Powell did in the Bakke case? Would she vote that way today, given the rapidly accumulating evidence of how the end of affirmative action in Texas and also in California, under state policy there, is resegregating the top public law schools? No one is sure.

Justice O'Connor ''would like to have diversity, but she doesn't want to have to talk about how you get there,'' Pamela S. Karlan, a law professor and voting rights expert at the University of Virginia, said in an interview. ''She's not at all indifferent, but she has almost an esthetic dislike of the nasty ugliness of taking race into account.''

There are some obvious differences between the Bakke and Piscataway cases. Allan Bakke lost an opportunity, while Sharon Taxman lost a job, which a majority of the Court may find unacceptable.

Bakke was a constitutional case, requiring the Court to apply the 14th Amendment's guarantee of equal protection of the laws to the new context of ''reverse discrimination.'' The Piscataway case is statutory, the question being whether the school board's action violated Title VII of the Civil Rights Act of 1964, the core Federal law that prohibits discrimination in employment. While the Constitution is binding only on government, Title VII applies throughout the private sector as well, to every workplace with at least 15 employees.

The Bakke case was about diversity among students, the Piscataway case about diversity within a faculty -- specifically, within a single high school department. Debra Williams and Sharon Taxman were the two junior members of the 10-teacher business department, equally qualified and with the same seniority. But Ms. Williams was the department's only black teacher, and when the order came to shrink the staff by one, the school board chose to retain her as a way of preserving diversity. Because there was no history of discriminatory hiring by the school board, neither side ever tried to describe the action as a remedy for past discrimination.

Two lower Federal courts ruled that the school board had violated Ms. Taxman's rights under Title VII, with the United States Court of Appeals for the Third Circuit, which sits in Philadelphia, writing broadly that under Title VII, diversity can never be a valid rationale for affirmative action. Only remedies for past discrimination ''can co-exist with the act's anti-discrimination mandate,'' the appeals court said in its 8-to-4 opinion last August.

Taken literally, Title VII's prohibition against adverse employment actions on account of race would bar nearly all policies that come under the heading of affirmative action. But the Court has nonetheless upheld affirmative action to alleviate a ''manifest imbalance'' in a work force and to remedy an employer's past discriminatory conduct.

In the mid-1980's, the Reagan Administration pushed a number of affirmative action cases to the Court in an effort to secure a ruling that would have permitted only identifiable victims of proven acts of past discrimination to benefit from affirmative action. The Administration's attempt failed, in part because Justice O'Connor, departing from the Court's other conservatives, insisted in her separate opinions on keeping the door open somewhat wider. How much wider is now the question.

Her concurring opinion in a 1987 case, Johnson v. Transportation Agency, upheld the promotion of a woman over a marginally better-qualified man for a public works job that no women had ever held. Citing the extreme statistical disparity, Justice O'Connor said the employer had ''a firm basis for believing that remedial action was required.'' Justice Antonin Scalia objected in a dissenting opinion that Justice O'Connor's position was little more than ''a halfway house'' on the road to race-neutral public policies.

In a 1986 case, Wygant v. Jackson Board of Education, Justice O'Connor agreed with the 5-to-4 majority that invalidated a public school district's policy to protect some recently hired black teachers against layoffs. The school district defended its policy as necessary to remedy ''societal discrimination'' and to provide black ''role models.'' But while agreeing that neither goal was valid in this context, Justice O'Connor noted in her separate opinion that the case left unresolved the validity of ''the very different goal of promoting racial diversity among the faculty.'' Because the school board had not raised that question, she said, ''I do not believe it necessary to discuss the magnitude of that interest or its applicability in this case.''

The language was typical O'Connor. ''She's defined herself as a judge who decides cases,'' Cass Sunstein, a law professor at the University of Chicago, said in an interview. ''She's nervous about rules and abstractions going wrong. She's very alert to the need for the Court to depend on the details of each case.''

Justice O'Connor's frequent refusal to go further than necessary to decide the case at hand has led some Court watchers to predict that she will keep the Court from using the Piscataway case to make a broad pronouncement if the Justices are in general agreement that the lower court can be upheld on narrower grounds. To say that diversity did not justify dismissing Ms. Taxman is not to decide whether diversity could ever be an acceptable rationale.

Four members of the Court -- Justices Scalia, Clarence Thomas, Anthony M. Kennedy, and Chief Justice William H. Rehnquist -- may well want to issue a definitive rejection of the diversity rationale, but ''they won't get her,'' Prof. Suzanna Sherry of the University of Minnesota Law School predicted. ''In a case that doesn't require it, she won't reach it.''