Courage Man has an important post, trying to work out the possibilities in the future:

I think the Church in Britain now, and thus the Church in the US sometime soon, really only has two options in the long run, though it should still do whatever it can do to kick the can down the road and delay The Day of Reckoning:

(1) simply close up shop, with respect to any charitable work that requires cooperation with Caesar, on the grounds that Caesar is fundamentally corrupt. That would mean closing down basically all of the Church’s charitable work. Running a hospital, for example, requires state licensing on practically every employee or procedure. Even a poor-relief center has licensing hoops to jump through (mostly pro-forma, but nevertheless). The Church in the US recently had the power to make Caesar back down with this threat. As when Cardinal O’Connor threatened to close all the New York Catholic hospitals rather than obey some proposed city regulation on contraception or abortion (the precise nature of which is evading my memory). The city promptly backed down, at least with respect to Catholic hospitals.

or
(2) refuse to obey Caesar and dare him to do his worst. In Scotland and Northern Ireland, the Church has hinted that it might do that and create "gay-rights martyrs." The pictures of nuns being arrested and Catholic schools being emptied would, one hopes, shame Caesar into backing down (maybe this is why the Church there may have won the minimum concessions that religious freedom requires). I don’t wish martyrdom on anyone, even though jail time, not drawing-and-quartering at Tyburn Field, is the worst it could realistically be. And I don’t see (1) as an acceptable end game either, as the Church’s social work is both valuable to the common good and too integral to the Church’s very self-understanding to be lightly tossed aside.