I'm not sure the Church is really concerned about the Constitution; it is a global, if not universal, religion. IMHO - Obama isn't stupid and he won't endanger his reelection chances. He made this move to extract something from the Church, as opposed to just giving away an exemption. Obama owns the MSM and will control the dialogue. The Church has a history of cutting deals with "state control" oriented people like Obama* and will probably just do that again. Obama knows the history.
Don't be surprised if you see photo's him signing something before the election with Catholic Church leaders standing beside him smiling. The agreement will limit Church power in some way and the Church will get an acceptable exemption. The media will spin it for Obama.
* Yes, Mussolini and Hitler, but I didn't want to upset readers before I made my point.
What religious freedoms did the Catholic Church give up to Hitler or Mussolini?
You must think Obama is the only one who remembers history. Study up on how many Catholics were martyred under the Communists and the Nazis sometime.
an aside: When I was a kid, a parish priest, Father Tony, was a 'guest' at one of Hitler's numerous 'Vacation Camps and Spas'. /s