What Is Extraordinary Care?

Everyone just assumes that, had Terri Schiavo made a clear statement of her wishes, it would be perfectly ethical and moral to do so. I am not sure that it wouldn't be, but I am starting to question that basic premise. A person certainly has the right to refuse any medical treatment, especially surgery. That being the case, the original insertion of a feeding tube, a surgical procedure, could certainly be refused. Once it is inserted, however, can they demand a surgical procedure (removing the feeding tube) that would result in their death? Is this any different than requesting an injection that would result in their death? I think that a strong argument could be made that a doctor could, and perhaps should, refuse such a request.
One could argue, however, that removing someone from a respirator would also be the same. Here, however, I think that a distinction can, and should, be made. Breathing, like the function of most organs, is an autonomic reflex. You do not have to think about doing it, and can be completely unconscious and continue to do it. Eating, however, requires an active effort. You have to tell yourself to eat. It seems to me that this is a significant distinction. If someone can no longer physically do something that doesn't happen automatically, and we have it in our power to assist them, isn't there an obligation to do it?
Update: I have since learned that in some cases, food injested through a feeding tube can end up coming up the esophogus, then back into the lungs, causing pneumonia. In any case that a feeding tube would cause harm to the patient, its removal would certainly be ethical.