The constitutional text flatly states that children born in the U.S. are citizens, without reference to whether their parents are aliens or not.
Then shall we see what the author of the amendment actually meant? From the floor speech of Senator Jacob Howard (R-MI) who actually wrote the amendment:
Every person born within the limits of the United States, and subject to their jurisdiction is, by virtue of natural law and national law, a citizen of the [United States]. This will not, of course, include persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers, accredited to the government of the United States, but will include every other class of persons.The Court read the 14th Amendment to recognize the existing American practice of granting citizenship based on birthplace. It saw no support for a new exclusion of the children of aliens. The Fourteenth Amendment affirms the ancient and fundamental rule of citizenship by birth within the territory, in the allegiance and protection of the country, including all children here born of resident aliens.
In U.S. v. Wong Kim Ark his parents were legal residents. No one is arguing against these. The question is that of those here illegally, i.e. those who are legally not residents. By law they are merely transient aliens, not residents. The precedent of the Kim case does not apply.
Then how can Marco Rubio or Bobby Jindal be citizens? Much less natural born citizens?