Lawyers for the administration and two groups of lawmakers from the House and Senate, nearly all Republicans, separately made that argument in briefs to the Supreme Court this week. The high court should relax the constitutional limits on religious invocations at government meetings, they argued.

The case could lead to a major change in the law on religion that would go well beyond prayers at council meetings.

Last year, a federal appeals court ruled that the town of Greece, N.Y., near Rochester, had crossed the line and violated the 1st Amendment's ban on an "establishment of religion." For years, the town supervisor had invited a local minister to deliver an opening prayer at the council's monthly meeting. Members of the audience were encouraged to join in the prayers.

Two residents, one Jewish and one an atheist, had complained for several years that the prayers were offensive and inappropriate. Until they sued in 2008, only Christians had been invited to lead the prayers.

Looked at through the eyes of a "reasonable observer," the town's prayer policy "must be viewed as an endorsement of … a Christian viewpoint," the U.S. 2nd Circuit Court of Appeals said in ruling against the town.