How is it permissible to let a woman die rather then perform an abortion?

So, I’ve been in a few debates recently on Fluther about the various republican bills trying to make their way through congress, but one hasn’t come up as much: H.R. 358 or the “Protect Life Act”. Currently, EMTALA states that a hospital can refuse to give an abortion on ‘conscience’ terms. However, they must get the woman to where she can be treated. HR 358 would remove the stipulation, and make it so a hospital can simply toss the woman out on the street.

Now, here comes the real question. I had thought this was ridiculous, really. Who would let a woman die like that? So I had somewhat ignored it. However, apparently this is not the case. Middle of last year, a nun was excommunicated for allowing a life-saving abortion to be performed.

So my question, dear flutherites: how is this possibly morally defensible? How can letting a woman, only in her first trimester, and with an “almost 100% chance of death” from heart failure die, be the morally correct choice?