I think this is a different situation from those here illegally. LEGAL visitors ARE "subject to the jurisdiction of the United States". If they drop the kid during the LEGAL visit, then current law applies. NO illegal immigrant, simply by virtue of their "non-documented" status is "subject to the jurisdiction of...".
I agree that the practice should be terminated, but I don't think you can equate the two situations.
Just being in the country does not make one "subject to the jurisdiction of the United States."
At least not by the definitions used when the Constitution was written or by its intent.
The 14th Amendment has been terribly misinterpreted as has been written about at length. Here are some links Carry_Okie posted the other day where he has encapsulated the issues.
"Birthright Citizenship": A Fraud on the Constitution
NO WAY. VISITORS here retain their allegiance to their homelands and so are NOT “subject to the jurisdiction” of the United States, which is what that phrase means. The discussion surrounding the adoption of this covered that very topic, IIRC!