"Compliance with the injunction would force the United States to go into violation of an international treaty designed to prevent drug trafficking worldwide, which could have both short- and long-term foreign relations costs and could impair the policing of transnational drug trafficking involving the most dangerous controlled substances," acting Solicitor General Paul Clement wrote in a court filing.
Here's Prof. Marci Hamilton's excellent analysis of the legal issues in the case, including why there is no claim under the constitutional Free Exercise clause and how the Court of Appeals could rely on the Religious Freedom Restoration Act after City of Boerne v. Flores (which held that Congress's Fourteenth Amendment power did not support the act). Hamilton, you should note, is a strong advocate for the government's side of the argument.
UPDATE: The United States has won a stay:
Justice Stephen Breyer, acting on behalf of the full court, granted a temporary stay to give both sides time to file more arguments with the court.