Should states be fighting Obamacare on religious grounds?

Great Debates
1

I’m just spit-balling here, but at 1st blush I don’t necessarily want my state (Ohio) joining a federal lawsuit challenging birth control coverage in Obamacare because it may offend religions, including mine (Roman Catholicism), or religious-based schools including my alma mater (Notre Dame, “Go Irish!”).

The story of the lawsuit from NPR is here:

Link.
Leaving aside the issue that ND is in Indiana and not Ohio, if Notre Dame doesn’t like the law - and it doesn’t - shouldn’t it bear the burden of paying for the lawsuit to challenge the law on religious grounds, and not the State of Ohio and its taxpayers?

What do you smart people think?

2

To what extent are the states involved? Do they, for instance, pursue violators, distribute funds in some way, etc? Lots of federal programs are up to the states to comply with or otherwise enforce, so I can see how states may be of the opinion that they’re being asked to enforce, apply, or otherwise administer a law which is unconstitutional. My knowledge of the particular facts is very sparse, unfortunately.