The Supreme Court heard arguments for and against affirmative action in school admissions on Tuesday, but the final decision could boil down to just one of the nine justices.

Justices Sandra Day O'Connor is the court's perennial swing voter. Her decision could determine the first changes to affirmative action in a generation, changing how race is used in schools, the government and other sectors for the foreseeable future.

"It is very likely that it will be 5-4," UCLA law professor Eugene Volokh said of the court's eventual vote. "The question is, 5-4 which way?"

O'Connor's thinking may or may not reveal that answer. At Tuesday's arguments, she asked whether law schools could not consider race since they use so many variables to determine an applicant's status.

Tuesday's case involves whether the University of Michigan and its law school can offer an edge to black, Hispanic or Native Americans students by granting them extra points in their rating system over white students with equal credentials. The University of Michigan gives minorities 20 points on a 150-point scale. Most accepted applicants must earn 100 points to get in.

Admissions officers at the law school use a looser formula that tries to ensure each class has a "critical mass" of about 10 percent or 12 percent minority enrollment.

The college's attorney, Maureen Mahoney, told the court Tuesday that a diverse student body is a worthy goal.

"The education of all students will be enriched. That is not a quota," she said in response to a question from Justice Antonin Scalia.

Scalia said the university, in creating such hard-access to the school -- admitting only 350 of the some 4,000 applicants each year -- set itself up for a situation that would result in racial imbalance.

The case was brought about by three white students who said they were passed over in favor of minority students on the basis of race. 

Solicitor General Theodore Olson, the Bush administration court lawyer, who has sided with the white students, said the law school program "is a thinly disguised quota. They're using stereotypes in an effort, they say, to break down stereotypes," he said.

The Bush administration filed its own brief, saying the Michigan program is unconstitutional because it "unfairly rewards or penalizes students based solely on their race."

The administration's brief did not call for an outright ban on affirmative action. In fact, it praised the goal of achieving racial diversity on campus.

It did, however, say that other means of achieving racial diversity would be preferable -- for instance, Texas' program of guaranteeing college admission to top students from every public high school. That program guarantees minority students from urban settings a shot at college.

Attorney Kirk Kolbo said the goal of promoting diversity on campuses is not a compelling reason to justify giving preferential treatment to minorities. His assertion was challenged right away, particularly by Justice Stephen Breyer, who said efforts to reach out to people of all races in order to make schools more diverse and to train minorities to be leaders in law, military, government and other fields is justifiable.

Tuesday's hearing was accompanied by thousands of demonstrators outside the court, mostly in favor of affirmative action policies. Among the speakers was the Rev. Jesse Jackson, who said there are more blacks in prison than in college.

"Young America, fight back," Jackson said.

Demonstrators chanted slogans in favor of the school policy. "They say Jim Crow, we say hell no" was one such chant.

"Affirmative action helped me, and I'm here to support students from all over the country," said Rosa Clemente of New York City. "The Supreme Court needs to do the right thing and support affirmative action," added Clemente, who described herself as a "black Puerto Rican" with degrees from the State University of New York at Albany and Cornell University.

The case has also prompted a barrage of briefs to the high court, both supporting and denouncing the policy. 

The university, backed by nearly 100 House Democrats and several former military officials, who wrote briefs in support of Michigan's policy, said the goal of student diversity should be sanctioned by the government, which has an interest in further improving race relations and universal education.

The court's ruling -- which could come in July -- will apply only to public, tax-supported institutions, but it could also spawn a ripple effect in private colleges and universities, government bodies and the business world.

Tuesday's arguments were directed to O'Connor, lawyers said.

"Who are they talking to? The answer is Justice O'Connor," said Nathaniel Persily, a constitutional law professor at the University of Pennsylvania.

"Justice O'Connor has proven herself to be the swing vote on previous affirmative action cases and in other cases dealing with race-consciousness in government programs," such as government contracting and legislative redistricting in the South, he said.

O'Connor, a moderate conservative named to the bench by former President Ronald Reagan, supported President Bush in Bush v. Gore, the case that effectively settled the 2000 presidential election. She has also joined the bench's more conservative judges on several other polarized rulings.

However, she has been known to join the court's four more liberal justices on several issues. Those four -- Justices John Paul Stevens, David Souter, Ruth Bader Ginsburg and Breyer -- are expected to support the university in the case.

Many lawyers expect Chief Justice William H. Rehnquist and justices Scalia, Anthony Kennedy and Clarence Thomas to decide the program is unconstitutional.

The Associated Press contributed to this report.