The founders could have never fathomed that we would be electing people to ANY government office whose parents were not American Citizens.
This shows exactly how superficial the world we live in really is. There are no deep roots to our society. We have chia pet politicians.
That's why the Preamble says that he Constitution was "ordained and established... to secure the Blessings of Liberty... to ourselves and our Posterity."
"Ourselves" means "We the People," the citizens of the United States who established the Constitution and delegated our powers to the states and the federal government.
"Our Posterity" means the children born to We the People.
Resident aliens are not "We the People," as they are not citizens and cannot vote for Representation in the House. Therefore, the children of resident aliens are not the "Posterity" of "We the People." Since resident aliens are expected to be here for a long time, it is reasonable to assume that they will have children. Their children may be born here, but they are not citizens descended via parentage, as their parents are still citizens of their home countries. They are not the Posterity of We the People.
It gets even murkier when the parents aren't even resident aliens, but people on temporary visas, such as tourists, students, and specialty or seasonal workers (L1, H-1B, H-2B).
-PJ