"The decision in Hobby Lobby rested on the premise that these accommodations 'achieve all of the Government's aims' underlying the preventive-health services coverage requirement 'while providing greater respect for religious liberty,'" the Justice Department wrote, quoting from Justice Samuel Alito's majority opinion. The legal filing was in opposition to an emergency plea from Wheaton College in Wheaton, Illinois, to avoid having to fill out Form 700. Wheaton is one of only a few nonprofits not to have won temporary relief in its court fight.

Rienzi, who also represents Wheaton, wrote in reply that the government is wrong to assume that the Hobby Lobby decision "blessed the accommodation." He noted that Alito specifically said the court was not deciding whether the administration's workaround for nonprofits adequately addressed their concerns.

On Thursday, the court, with three justices dissenting, allowed Wheaton to avoid using the form while its case remains on appeal. Instead, the college can send written notice of its objections directly to the Health and Human Services Department rather than the insurer or the third-party administrator. At the same time, the government can take steps to ensure that women covered by Wheaton's health plan can get emergency contraception the college won't pay for.

Several legal experts said that perhaps a simple revision to the government document at the center of the dispute could resolve matters.

"I think the question will come down to does the government really need them to tell the insurance companies or can you reword the form," said Marc Stern, a religious liberty specialist and general counsel for the American Jewish Committee. The faith-affiliated charities "might win a redrafting of the form. I don't think they can win an argument that says we can do absolutely nothing," Stern said.

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Zoll reported from New York.

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