Yes. But the issue is whether (free) contraceptive coverage, abortifacients and sterilization fall under the expectation of universal coverage the way that say treating someone for a gunshot or cancer might.

Previously when the State has tried to force the Church's hand on this issue the Church has been able to dodge the issue either by self-insuring or removing itself from providing services. I don't know what the rank and file Catholics think but the leadership is adamant that they will not comply with this mandate. That would mean either closing down institutions or refusing to provide coverage for anyone. Some might think they're playing "chicken" but I don't think so.

Contraceptives are already pretty cheap and easy to obtain. It seems needlessly provocative to attempt to force religious institutions to pay for and/or provide instructions on how to obtain items which are anathema to them. Although PP is not a religious institution (though some people seem to have the same level of devotion one would normally associate with a church), imagine if the HHS under a President Romney or President Santorum determined that contraception was not medically necessary and thus every institution was hereby prevented from purchasing a plan that included it. PP would hit the roof. Or imagine if it was medically proven that alcohol and pork cured cancer and every business was then required to provide free drinks and ham in its cafeteria. Kosher and halal would get no exemption. Or... you get the point.

Every religious group has rules, which may seem silly to outsiders or may in fact even be silly, but under the First Amendment, they should have a right to follow those rules, absent breaking the law in some other aspect. The Church is not preventing anyone from getting bc; it's just saying we're not providing it/paying for it.