Having worked for two separate Catholic organizations over the last fifteen years my experience was that no form of birth controlled was approved including vasectomy. At one point during my tenure with one of the agencies my family had a miscarriage and initially the insurance company would not cover the cost because of the medical coding as it was not part of our insurance program. When I worked for Catholic organizations I understood that I was accepting a position with a group affiliated with the church and by that I understood that my employment would, in some measure, be dictated by the moral positions the church and organization held.
The problem that I see with this is that we (the government) are forcing a group to participate in something that is against the mandates of the belief they hold. While it is true that the individual employees would not be required to utilize this service the organization as a whole would still be billed at a rate that includes this option. I don't see this as acceptable and hope any religious organization that request it will be granted a waiver and not forced to pay for something that goes against the moral position they have taken. I believe that if these groups are not given a waiver what you will see is that many of them will simply drop health care and pay the penalty, forcing the employees into the government controlled policy. Should this happen, I would expect that it would create a huge spending issue to the government - which would get us back to the beginnings of this thread; financial issues.
I fear that many will make this an issue of the Church attempting to limit access of women to birth control. However, this is simply not true as the Church is not limiting access to anyone - there are of course - doctors, clinics, health departments and so on that employees of faith based organizations can (and I assume do) go to. Access is not denied but the organization simply is standing on the principals they hold and saying - no, we shall not pay for that. Something that I believe they should have the right to do.