The US Supreme Court plunged into treacherous constitutional waters Wednesday as the justices took up a case examining whether the practice of conducting a prayer before a town board meeting violates the separation of church and state.

How the high court answers that question could have a profound effect on the content of religious invocations offered at gatherings across the country, from daily sessions of Congress and state legislatures, to town councils in the smallest of hamlets.

By the conclusion of the hour-long oral argument it was clear that the court was sharply divided over the First Amendment implications of conducting overtly Christian prayers at the start of town meetings.

What was less clear was how the high court is likely to resolve the case.

At issue in Town of Greece v. Galloway (12-696) is the longtime practice of inviting a volunteer to deliver an invocation prior to each monthly board meeting.

Greece is a suburb of Rochester in upstate New York. The town offers no advice to would-be prayer givers and does not seek to alter or water-down the religious content of any prayer. Anyone who volunteers is allowed to give a prayer.

Although many members of the community – and town board members – willingly participate in the prayer activities, not all residents support it.

Two residents objected and filed suit charging that the town was violating the First Amendment’s Establishment Clause by forcing everyone at the town meeting to participate in an unwanted religious activity.

A federal judge disagreed and upheld the prayer practice, but the Second US Circuit Court of Appeals sided with the objecting residents. The appeals court found that prayers offered at the board meetings were overtly Christian and that the ongoing practice of featuring such prayers at town meetings amounted to an unconstitutional endorsement of Christianity by the local government.

Justice Elena Kagan began Wednesday’s oral argument session with a dramatic hypothetical question. She wanted to know if it would be permissible for the chief justice to call a minister to the front of the courtroom, ask everyone to rise, and deliver an overtly Christian prayer.

She read one of the prayers offered before a Greece board meeting: “We acknowledge the saving sacrifice of Jesus Christ on the cross. We draw strength from His resurrection. Blessed are you who has raised up the Lord Jesus. You will raise us in our turn and put us by His side.”

After that, Justice Kagan said in her hypothetical example, the justices who were standing would make the sign of the cross and then the chief justice would call the first case.

“Would that be permissible?” Kagan asked Thomas Hungar, the Washington lawyer representing the Town of Greece.

“I don’t think so, Your Honor,” Mr. Hungar replied. He quickly added that Kagan’s fact pattern was substantially different than the case involving the Town of Greece.

The case before the high court, he said, involved legislative prayer, which has been a national tradition as old as the country and which the US Supreme Court approved in a 1983 case.

A few minutes later, Justice Anthony Kennedy returned to the Kagan hypothetical. He wanted to know why Hungar agreed so quickly with Kagan that her example was unconstitutional.

“You seemed readily to agree that that would be a First Amendment violation,” Justice Kennedy said. “Why?”

Hungar tried to backtrack. “Well, perhaps I conceded too much…,” he said.

Kagan’s hypothetical and Kennedy’s response to it illustrate the depth of disagreement among the justices over how best to resolve the looming First Amendment issues raised in the case.

On one side of the court, justices Kagan, Ruth Bader Ginsburg, and Sonia Sotomayor view the prayers offered at the town board meetings as overtly religious and posing a significant threat of coercion.

It places residents about to appear before the board in the position of risking the ire of board members (and losing votes) if they refuse to participate in a public prayer that is obviously important to board members.

On the other side of the court, Chief Justice John Roberts, and Justices Samuel Alito, Antonin Scalia, and Kennedy appear more concerned about the problem of the government trying to fine-tune an expression of religious belief – or to censor it.

Douglas Laycock, a University of Virginia law professor representing Greece residents opposed to the public prayers, suggested that the town board should advise potential prayer-givers to avoid religious subjects on which believers are known to disagree and keep their prayers nonsectarian.

“There’s a long tradition of civic prayer and the clergy know how to do it,” said Professor Laycock, a leading church-state scholar.

The conservative justices weren’t so sure. Justice Alito asked Laycock to provide an example of a prayer that would be acceptable to the full range of diverse faiths in America today. He named a few: Christians, Jews, Muslims, Buddhists, Hindus, Wiccans, and the Baha’i.

Justice Scalia added: “And atheists. Throw in atheists, too.” The courtroom erupted in laughter.

Laycock said that a third of the prayers offered at Greece town meetings would be acceptable. He suggested that prayers to “the almighty,” would fit.

Alito questioned whether those who believe in more than one god would accept “the almighty” as the focus of a prayer.

“What about devil worshipers,” Scalia wanted to know. Again, there was laughter in the court.

“Well, if devil worshipers believe the devil is the almighty, they might be okay,” Laycock said. “But they are probably out.”

In the end, it was unclear how a prayer – a sincere expression of faith – could be fashioned that would be acceptable to most, if not all, religious sects.

“We have a very religiously diverse country,” Alito said.

He said all religions should be treated equally, “but I just don’t see how it is possible to compose anything that you could call a prayer that is acceptable to all of these groups.”

Scalia said the case also involves the other religion clause within the First Amendment – the clause that protects the free exercise of religion.

He said that town board members serve as citizen-legislators and have a right to invoke the deity before undertaking serious governmental tasks.

“There is a serious religious interest on the other side of this thing that people who have religious beliefs ought to be able to invoke the deity when they are acting as citizens,” he said.

“When they do that, so long as all groups are allowed to be in, it seems to me an imposition upon them to stifle the manner in which they invoke their deity,” he said.

Laycock responded that such citizen-legislators are free to pray before any public meeting, or to pray silently any time they feel the need.