There is no statute giving these children citizenship, only some contorted reasoning in a footnote by some S/C justice circa 1980s. Sorry, I am so fuzzy on the details, we both should look this up.
The current statute (8 U.S.C. 1401) tracks the language of the 14th Amendment, but it has been interpreted by every administration, Republican and Democrat, since at least the 1920s, to grant citizenship to children born here of illegal alien parents.
Plyler v. Doe