I'm a a Constitutional Originalist. So, no.
As such, you have to go by the meaning of words and the speachifying of the 14th amendments proponents which leads to children of citizens (naturalized or born here) are also citizens. At the time of passing the proponents of the amendment wrote as such to mean children whose parents were not subject to any foreign power. Therefore, the parents could not be citizens of another country. 1898 United States vs Wong Kim Ark pretty much assumed that if you were a LEGAL immigrant you were not subject to a foreign power any longer.
The case less than 100yrs later... 1982 Plyer vs Doe pretty much said Legal/Illegal...Toe-mato/Toe-Mahto... what's the dif? Eh? And here we are.
Just as the court was wrong in Plessy vs Ferguson, so they were also wrong with Plyer vs Doe (and Roe vs Wade, go look, there is no "right to privacy" in the Constitution).