He'd have to close down all the Christian hospitals first...but I can see that happening. If FOCA causes lawsuits everywhere to force all medical facilities to offer abortions, Christians will close or sell out. (Which would be pretty horrible to start with, as the most efficiently run not-for-profits just happen to be those owned by Christian groups.)
Of course, most Christians will get out of healthcare period, so he probably won't have much trouble enforcing his no-free-speech hospitals. Certainly not in comparison to the trouble he'll have in finding staff for them...