The risk for the illegal alien's kids who were born in the United States is that an administrative process can be abolished with the flick of an administrator's wrist when any revision to the set of rules in which it is lodged is passed around for review.
Birthright citizenship could simply disappear as if it had never existed. In virtually all cases, unless there has been some challenge along the way, when an administrative process changes or is abolished, the effect is not only instantaneous it is retroactive.
That's because it's not the sort of statutory or judicial process "law" that's prohibited from being made retroactive.
Let's say the State Department's rules are changed (by appropriate legislation if needed, although I think the Hildabeast can do this on her own) and all at once there never was a process that resulted in a determination that mere birth in this country sufficed for State Department purposes, to wit, issuance of passports.
The next time one of those guys gets his American passport renewed, he can't get it. He's not a citizen ~ nor was he ever a citizen ~ and he'll be referred to ICE for further disposition.