This is really the whole thing, regardless of how developed the baby is.

Imagine a fully formed child or adult with a liver problem. Science comes up with some way that someone of similar genetics can be physically connected to them and filter their blood for them and keep them alive while they wait for a transplant. Should the person who can physically sustain another person's body be legally required to do so?

So far, less invasive versions of this say no: https://en.wikipedia.org/wiki/McFall_v._Shimp

You can't even force dead bodies to donate organs.