What apparently is tucked into the Stupak amendment, and is the big bone of contention, is this bit that requires that any insurance company that participates in the exchange has to offer the same policies in the exchange as it does in the open market to prevent insurers from offering substandard policies to the poor while extending better policies to those who are better off. So, assuming a big chunk of the insurance market action will be on the exchange, every insurer will want to participate, meaning they they would have to get rid of abortion coverage in all their policies that they offer.
The Stupak amendment wasn't just to make sure that the Hyde Amendment stood-- which prohibits federal funding of abortions and has been around since the 70's. This was to prevent insurance companies from providing abortion coverage PERIOD in either a policy or a rider.
So, it was no surprise that the US Conference of Catholic Bishops supported and lobbied for the Stupak Amendment. It doesn't make them any different than any other pro-life group with the exception of making a statement to all women that regardless of your religious beliefs, it doesn't matter, and that our way is the right way. Is that the message the Catholic Church wants to espouse?