Among the plaintiffs is Hobby Lobby, a nationwide chain of about 500 for-profit arts and crafts stores. David Green and his family are the owners, and say their Christian beliefs clash with parts of the law's mandates for comprehensive coverage. They say some of the drugs that would be provided prevent human embryos from being implanted in a woman's womb, which the Greens equate to abortion.ADDED: Full CNN story here.
AND: Note that the claim is based not on the Constitution, but on the Religious Freedom Restoration Act, a federal statute. Congress can change the statute. That counts heavily in my book.