Do you really believe that the Catholic church won't cave? I think they will grumble and let this "compromise" stand without too much more sound and fury.
Unfortunately, too many Catholics (including leadership) agree with leftist governance. They may be angry about this specific thing, but provide them enough cover and they will fold. Face it, probably a majority of Catholics and even more in leadership like Democrats far more than Republicans - and they really WANT to like Obama. They fall all over themselves to find reasons to support him.
One can see the trap a million miles away. The Hussein administration will say it compromised and found a "balanced" approach. The Catholic church will back off to the point they are not a useful ally in the fight. Meanwhile millions of women will want their freebie contraception and love that Obama is giving it to them (even many supposedly right of center will like this just like everyone who gets a freebie does). Republicans will continue to fight but without the church actively supporting them, they will just appear to be trying to take a new right to free contraception away.
I've absolutely zero faith in the Catholic church to continue this fight.
I'm a bit more optimistic, although the Catholic Church has already committed a historic blunder, which cost them millions of parishoners. This issue can only make that worse.
Christian churches in the US are, and have always been, fully funded by its parishioners, not by the Vatican or Riyahd.
When the Catholic Church abuse scandal was at its peak, instead of vigorously fighting the multitude of multi-million$ suits that resulted, it was no skin off the Vatican's nose to allow the financial burden to fall entirely on the parishioners. The parishioners had absolutely no control over the abuse. The worst possible reaction.
I never left the Catholic Church. It left me. Yes, I am still very much a Catholic, and satisfy my Catholic obligations by other means.