Right or wrong (I think it’s wrong), the way the current law is written, the infant of illegal aliens, if that infant is born in the USA, is a natural born US citizen.
See paragraph “a” in post 128, which is a copy/paste of Title 8, Section 1401 US Code.
That’s why folks get upset over “anchor babies.”
Some lawyer can feel free to correct me, if I’m wrong.
The word "natural" (and therefore the legal term of art, "natural born citizen") does not appear in 8 USC 1401. 8 USC 1401 defines "citizenship," and that terms appears as a qualifier for Congress.
-- That's why folks get upset over "anchor babies." --
Not exactly. The anchor baby phenomenon irks people because the babies are used to give immigration/naturalization preference to people who broke the immigration laws in the first place.
The qualification for the presidency is an issue that occurs infrequently, and to a small fraction of the population.
While the location of birth is highly relevant in a citizenship inquiry (countries tend to want to "control" everybody born on their turf), the citizenship of parents is ALSO highly relevant, and in some cases is absolutely determinative.
Naturalization Act of 1790 (http://pds.lib.harvard.edu/pds/viewtext/5596748?op=t&n=1)
And the children of citizens of the United States that may be born beyond fea, or out of the limits of the United States, fhall be confidered as natural born citizens: Provided, That the right of citizenfhip fhall not defcend to perfons whofe fathers have never been refident in the United States