I am on the fence here....
In theory I like the concept as my state is suffering over illegal healthcare, education, and jobs.
However the place of birth being your national identity is so historically founded that I am hesitant to alter the tradition of entitlement. I would be happy to see a citizenship not applicapable until the person is 18, thus to be raised by their parents in the parent's native country and being given a choice of assuming one final citizenship upon becoming a legal adult by US standards (we could DNA type the infant before they were deported with their parents for future confirmation of identity).
Here is a thought why not just enforce the laws we already have and if any alteration is needed then speed up the deportation process and consider upping fines toward individual violators (resulting in imprisonment if caught again on US soil illegally and not being able to re-enter legally until those fines are paid) as well as fines to the country of origin.