Nonsense. Offspring of illegal aliens are not "subject to the jurisdiction thereof".
http://federalistblog.us/2007/09/revisiting_subject_to_the_jurisdiction.html
Except for the children of accredited diplomats, anyone born on US soil is a US citizen, i.e., jus solis. That is the way our laws are written and practiced, which is why we have 400,000 anchor babies born each year who are entitled to such things as US passports and food stamps.