ASHINGTON, June 23 — The Supreme Court's rulings on the University of Michigan's admission policies today set off a wave of consternation among conservative groups, with officials of several saying they are now more determined than ever to demand President Bush choose someone whose opposition to affirmative action is crystal clear to fill any vacancy on the court.

The individual who stands to lose the most from any energized campaign to seek a vigorous opponent of affirmative action is almost certainly Alberto R. Gonzales, the White House counsel, who is frequently mentioned as a likely choice to fill any court vacancy.

Although Mr. Gonzales has said very little publicly about his position, he is widely viewed by conservatives as a heretic on the issue and the person most responsible for blocking the White House from submitting a more hard-line brief on the Michigan cases to the court.

"This is a very political decision and the administration's brief played a crucial role, I believe, in influencing Justice O'Connor, who turned out to be the swing vote," said Linda Chavez, the president of the Center for Equal Opportunity, one of the groups that had challenged the Michigan programs. She was referring to Justice Sandra Day O'Connor.

"On a political level, this does highlight the importance of the appointment process, and I can tell you there are a lot of conservatives who believe there was one person who was the most influential person in this administration," she said. "That person was Alberto Gonzales, and it seemed he was really the key player in arguing for a down-the-middle compromise position before the court."

In fact, the administration's brief argued that both the admissions program at the law school, which was upheld, and the one at the undergraduate school, which was struck down, were unconstitutional. But the administration had included in its argument a statement that racial diversity is a worthwhile goal, a principal rationale behind the court's 5-to-4 ruling that the program at the law school was acceptable.

On a broader political canvas, the court's split decision certainly means a continuation of the rich and often-divisive debate as to when and under what circumstances members of minorities should be given extra consideration.

The American public is generally amenable to the concept of affirmative action, polls show, but less supportive when the programs more closely resemble flat-out quotas. A New York Times/CBS News poll conducted in January showed that 53 percent of those surveyed favored "programs which make special efforts to help minorities get ahead" to make up for past discrimination, with 39 percent opposed.

While the general public is tolerant of some level of affirmative action for members of minorities, conservative public policy groups and conservative political figures have urged the adaptation of a wholly race-blind policy that shuts the door completely on any advantage for race or ethnicity.

There is great scorn among those conservatives who form an important part of Mr. Bush's political base for any equivocation on such issues.

Many conservatives hold Justice David H. Souter, who was appointed by President Bush's father, in great disdain because he was sold to them as a reliable vote but has instead been a mainstay of the more liberal wing on the court, and who voted today in favor of both Michigan programs.

"It's outrageous that the majority in favor of these racial preferences was formed by Republican appointees," said Clinton Bolick, vice president of the Institute for Justice, a conservative group that helped challenge the Michigan programs. He was referring to Justices Souter; O'Connor, who was appointed by President Ronald Reagan; and John Paul Stevens, who was appointed by President Gerald R. Ford. The other two justices who were in the majority today are Steven G. Breyer and Ruth Bader Ginsburg, who were appointed by President Bill Clinton.

Mr. Gonzales, who grew up in a large, poor Mexican-American family and provides, White House officials believe, a warm personal story of overcoming adversity to attend Harvard Law School, is naturally thought of as sympathetic to providing extra consideration for members of minorities in university admissions programs.

But it was widely reported that in the internal administration debate over what stance to take before the court in the Michigan cases, Mr. Gonzales argued for a moderate approach, while the solicitor general, Theodore B. Olson, favored a firm opposition to consideration of race or ethnicity.

The swift acknowledgment by conservatives that today's rulings were a defeat for their cause provides a vivid demonstration as to how the perception of the issue has changed.

When the Supreme Court decided the first major affirmative action case, involving Alan Bakke, in 1978, it was perceived as a victory for opponents of affirmative action, because Mr. Bakke won admission to medical school, even though the court first enunciated its principle that racial diversity could be a worthwhile educational goal.