A privacy-rights organization faces an uphill battle to persuade the U.S. Supreme Court to halt the National Security Agency’s surveillance of domestic telephone records.

The Electronic Privacy Information Center (EPIC), a Washington-based nonprofit public-research center, on Monday filed a petition for a writ of mandamus, or, in the alternative, a petition for review, with the justices. It charged that the Foreign Intelligence Surveillance Court (FISC) exceeded its statutory authority under the Foreign Intelligence Surveillance Act when it ordered “production of millions of domestic telephone records that cannot plausibly be relevant to an authorized investigation.”