ASHINGTON, Dec. 2 — An argument by religious conservatives in a church-state case they embraced as a vehicle for expanding their recent Supreme Court victories met resistance from a deeply divided court on Tuesday. A majority of the justices expressed concern about the implications of requiring states to subsidize religious training if they choose to provide college scholarships for other kinds of study.

The court heard arguments on the validity of Washington State's Promise Scholarship Program, which makes awards on the basis of academic merit and financial need to students who attend accredited colleges in the state, including those with religious affiliations, but excludes students pursuing degrees in theology.

A federal appeals court, ruling in a lawsuit brought by a student who would have qualified for the scholarship had he not chosen a major in pastoral ministry, found the exclusion to be an unconstitutional burden on the free exercise of religion. Washington State's appeal of that ruling has produced a Supreme Court case of potentially landmark dimensions, raising the profound question of whether, and under what circumstances, the government can carve religion out of general programs of services and benefits.

The justices devoted much of the lively hourlong argument to probing for just what the consequences might be on issues like school voucher programs if they agreed with the appeals court. The two justices most often in the middle of the court's church-state debates, Sandra Day O'Connor and Anthony M. Kennedy, sought assurances that neither the student's lawyer, Jay A. Sekulow, nor Solicitor General Theodore B. Olson, arguing for the Bush administration as a "friend of the court" on the student's behalf, was willing to provide — that a decision to strike down the Washington program could stop there.

By the end, a clear majority of five or even six justices appeared unconvinced that a limiting principle would be available if they accepted the broad argument that the Constitution mandates equality in awarding government benefits to religious and nonreligious activities alike.

The limitation in Washington's scholarship program is required under the state Constitution's strict separation of church and state. Narda Pierce, the state's solicitor general, described the state Constitution as protecting "the freedom of conscience of all its citizens" by "not compelling its citizens to provide enforced public funds to support the promotion of religious beliefs with which they may or may not agree."

Washington is one of 37 states to forbid the public financing of religious instruction. Many such provisions mirror a failed federal constitutional amendment known as the Blaine Amendment, proposed in 1875 and widely regarded today as an expression of the anti-Catholic sentiment of the day.

But despite briefs urging them to regard the state provisions as the illegitimate expressions of religious bias, the justices expressed little interest in the past and great concern about the future.

"The implications of this case are breathtaking," Justice Stephen G. Breyer observed at one point to Solicitor General Olson, who called the Washington program "the plainest form of religious discrimination."

Although the issue was not mentioned directly, the administration's religion-based initiative would benefit immeasurably from a decision to uphold the ruling by the United States Court of Appeals for the Ninth Circuit. Not only would it be permissible to channel federal money through religion-based service organizations, but some version of the administration's program might be seen as constitutionally mandatory.

"If your side wins," Justice Breyer told the solicitor general, "every program, not just educational programs, but nursing programs, hospital programs, social welfare programs, contracting programs throughout the governments" would all be subject to the argument "that they cannot be purely secular, that they must fund all religions who want to do the same thing."

Different religious groups "may get into fights with each other about billions and billions of dollars," Justice Breyer continued.

Describing the Washington program, Mr. Olson said that "the clear and unmistakable message is that religion and preparation for a career in the ministry is disfavored and discouraged." He added, "the person who wants to believe in God or wants to have a position of religious leadership is the one that's singled out for discriminatory treatment."

His argument met an unexpectedly skeptical response from Justice O'Connor, who said: "Well, but of course, there's been a couple of centuries of practice in this country of not funding religious instruction by tax money." She added, "I mean, that's as old as the country itself, isn't it?"

Mr. Olson replied: "Well, yes it is. But there is the other tradition that is as old as the country itself, the free exercise component of the religion clauses, which this court has said repeatedly mandates neutrality."

At times, Justice O'Connor appeared to doubt that the state's denial of a scholarship for religious study amounted to an unconstitutional burden in the first place. "How does this violate the student's right to free exercise of religion?" she asked Mr. Sekulow, the student's lawyer. "Maybe it's more expensive to go to school, but why does that violate his free exercise of religion?"

Throughout the argument, both Justice O'Connor and Justice Kennedy worried aloud that a decision striking down the Washington program would have the effect of compelling any state that offered tuition vouchers in a "school choice" program to include religious schools, regardless of whether the state wanted such an inclusive program.

"Can they refrain from making that program available for use in religious schools?" Justice O'Connor asked Mr. Sekulow.

"I would think not," replied Mr. Sekulow, chief counsel of the American Center for Law and Justice, a legal organization founded by the Rev. Pat Robertson.

"So what you are urging here would have a major impact then, would it not, on voucher programs," Justice O'Connor said.

A decision by the court in June 2002 upheld a tuition voucher program in Cleveland that provides for participation by parochial schools and that was challenged as an unconstitutional "establishment" of religion. That decision raised, but did not answer, the further question of whether religious schools had to be included in such programs, which have spread more slowly than their proponents had hoped, in part because of the existence of state prohibitions like Washington's.

Justice Ruth Bader Ginsburg asked Mr. Sekulow a question that she described as "really what the case turns on." Is there "any space," she asked, "between what a state is permitted to fund under the Establishment Clause and what it must fund under the Free Exercise Clause and, if so, what fills that space?"

For example, she continued, could a state decide to subsidize the training of doctors, lawyers, architects, and members of all other professions except the clergy?

Not unless the state could show a compelling interest for making such a distinction, Mr. Sekulow replied.

For his part, Justice Kennedy seemed to be looking for a way to avoid the broader issue by finding the Washington program to be invalid on grounds that would not carry the same broad implications. Why could the program not be invalidated on the ground that it placed a burden on a student's "religious conscience," he asked, by forcing students to choose secular majors if they wanted the scholarship money.

But Justice David H. Souter suggested that a ruling on that basis would not avoid implications for the voucher question. If tuition vouchers were available only for nonreligious schools, he said, the argument could be made "that the religious student must somehow surrender a conscientious belief" and enroll in a secular school to use the voucher.

Joshua Davey, the student whose lawsuit led to this case, Locke v. Davey, No. 02-1315, continued his religious studies at Northwest College, which is affiliated with the Assemblies of God. He did not, however, become a minister. He is now a student at Harvard Law School, and attended the argument Tuesday.