Seven state attorneys general filed suit Thursday to block the White House mandate that religious institutions’ employee health plans offer birth-control services, the Associated Press writes.

The Republican attorneys general of Florida, Michigan, Nebraska, Ohio, Oklahoma, South Carolina, and Texas filed the suit, and two Catholic groups and a high school joined in the suit.

The lawsuit alleges that some religious employers would end up dropping health-insurance coverage, which would increase the number of people enrolling in state Medicaid programs and using state-subsidized hospitals.

The rule would not apply to churches but does cover many faith-linked nonprofit groups. After an initial outcry, the Obama administration amended the mandate to shift the cost of providing contraception from religious employers to insurance companies, but opponents of the rule, led by U.S. Catholic bishops, said the compromise does not go far enough.