Republicans and religious organizations fighting President Obama’s new birth-control-coverage rule are focusing their hopes on what could prove the next front in the battle: the courts.

Since November, at least eight lawsuits have been filed in federal district courts across the country challenging the constitutionality of the rule, which requires employers, including church-affiliated organizations that object to contraception on religious grounds, to cover birth control in workers’ health plans with no out-of-pocket charges. (Groups that are exclusively religious, such as churches, are exempt).