Eh, yes and no. A caregiver legally owes effort to a dependent. You can't neglect a child (or elderly person, or disabled person) until they die - that's a felony pretty much everywhere. Hell, neglecting a pet to death is felony animal cruelty in a lot of places.

So "only one matching donor in the world for a kidney/bone marrow/whatever" argument isn't exactly on point, because a caregiver is responsible to a dependent fat more than a random person would be. But a caregiver also isn't required to go to extraordinary lengths, either. So when looking at the situation from a caregiver perspective, the two questions are 1)at what point does a fetus become a dependent (which is an awful lot like the "at what point is it a person" question), and 2)is carrying a viable pregnancy to term ordinary support or extraordinary support? I don't have good answers for either of those questions, but hopefully it shows that the legal and moral principles are a lot muddier than "nobody owes somebody else a kidney full stop."