The founders were smart.
If both immigrant parents were citizens at the time the child was born, it may be acceptable. The issue then would be foreign allegiance, which should be extinguished when they take the oath of loyalty when they gain citizenship. Some nations like England did at the time of the American Revolution, did not recognize our citizenship, they were conscripted often because they were English Subjects.
Children of Foreign born parents who are not citizens have no claim.
If the parents become citizens first then they are no longer foreigners and their children are natural born citizens.
If they are still foreigners, then so are their children, even if born here and also awarded US citizenship under a misinterpretation of the 14th amendment.
The same principle that allows Ted Cruz to claim US citizenship while born in Canada applies to all the children of foreigners born here.
Natural born citizens are naturally citizens of the US because they could not be anything else, they are born here of citizen parents.
Anyone born with more than ONE nationality is NOT a natural born citizen.
http://www.art2superpac.com/issues.html