Lifted from a note from Beverly Mann in response to a query of mine, as a note of interest:
Here’s a link to a long Politico article on those cases and on the prospects of their success:
Apparently it looks like the Supreme Court eventually will hear two or three of these cases, probably all at one time, and draw some line about which organizations and for-profit companies are entitled to be exempt from the contraception part of the mandate. But mainly, these lawsuits concern a federal statute called The Religious Freedom Restoration Act, which provides religious protections for these groups beyond what the Supreme Court has held that the First Amendment requires. That statute was passed in reaction to a Supreme Court opinion that defined the First Amendment’s Free Exercise clause more narrowly than a majority of Congress thought was appropriate.
The Politico article gives a pretty detailed rundown on this.