The 14th Amendment says:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside.The bolded part, in the discussion of the amendment, was meant to exclude children of diplomats born in the US. It would also exclude foreign kings and other persons with diplomatic immunity. It would specifically INCLUDE children of legal immigrants.
An argument could be made that the clause would exclude babies born to people illegally in the US.
the 14th amendment didn’t exist at the time A2S1C5 was written. even if it did, it only addresses citizenship and not natural born status.
the point here is the definition of ‘natural born citizen’ as understood and meant by the founders.