Let's get it straight. The Affordable Care Act requires health insurers to cover contraception without co-pays. It does not, however, require religions, churches, parishes, dioceses, archdioceses, etc. to cover contraception -- they are exempt (if you're a secretary working for a church you're shit out of luck). What we're talking about are public institutions like universities and hospitals -- non-profit businesses (much in the same way that UPMC, for example, is a "non-profit") -- who take government money and who take money from the public being required to follow the law to not discriminate against women when covering their health care costs.
If the Catholic Church does not want to follow the law, they can stop taking federal funds or they can get out of the business of running businesses.
That's their choice.
(Jesus' choice -- from all available evidence -- would seem to be to sell everything and give it to the poor. Just saying...)