The court’s ruling in the Hobby Lobby case could also affect other kinds of laws. In a brief filed this month, Solicitor General Donald B. Verrilli Jr. warned the justices that a broad decision striking down the contraception provision could imperil minimum wage and overtime laws, Social Security taxes and vaccination requirements, all of which have been subject to religious challenges in earlier cases.

Another brief, from California, 14 other states and the District of Columbia, argued that such a decision would allow businesses to seek to deny coverage for blood transfusions, immunizations, treatments involving stem cells and psychiatric care.

But Michigan and 19 other states countered that protecting religious freedom is “as American as apple pie.” That freedom, they said, protects “a Jewish-owned deli that does not sell nonkosher foods” and “a Muslim-owned financial brokerage that will not lend money for interest.”

The justices will analyze Hobby Lobby’s challenge under the Religious Freedom Restoration Act of 1993, which requires the federal government to meet a demanding standard when it imposes burdens on religious beliefs.

Eighteen states have religious freedom laws similar to the federal one, and additional bills are pending in Hawaii, Missouri, Mississippi, Oklahoma and Wisconsin, according to a survey from the American Civil Liberties Union. Last month, Gov. Jan Brewer of Arizona, a Republican, vetoed a religious freedom bill after objections from business leaders and others who said the measure would have allowed discrimination against gays.

Douglas Laycock, a law professor at the University of Virginia, said he was worried that a ruling against the corporations in Tuesday’s case would threaten to unravel important safeguards in religious freedom laws. “The whole secular left has decided,” he said, that such laws “are very dangerous because they care so much more about the contraception cases and gay rights.”