At least one parent required to be a citizen? Unless it's both, you get into the dual citizenship problem. As I recall, the one citizen parent interpretation was developed out of thin air several years ago to try to legitimize Obama.
The parents do not need to be citizens; they merely need to have consented to be under the laws of the the USA — that is, legal residents.
Both of Rubio’s parents had green cards, and were fully subject to the laws (e.g., taxation) of the USA.