I’m with dpg on this. People are crossing the border now for this very reason, and some right wing extremist groups are going to great lengths to prevent them, by building walls and having militia groups patrolling the border.

In a post-apocalyptic world I don’t see how it would even matter where the baby is born, since everywhere would be just as bad. Also, there would quite possibly no longer be any governments and all borders would be meaningless.

One thing that COULD make it an interesting reason to set it in a post-apocalyptic future is if ? provided that there still were nations and borders ? the situation was reversed from now and the US was maybe a bit worse off than other places and people were desperately trying to get OUT of there, including the mother who instead wants the baby to be born in Mexico instead. If you flip the situation, then it might be a reason to place it in the future, otherwise you could just set it in the present.

There are two Discworld novels, with similar plots, you might want to read. Always good to know, so you can differentiate your script from those stories. First there’s “Mort” which might not be that much similar, but it is about Death getting an apprentice, and the second one is “Reaper Man,” where Death actually is fired, and takes a job on a farm because, after all he’s good with a scythe. Both novels are by Terry Pratchett.