The "anchor baby" situation is readily resolved by thinking of these guys as "tourists" rather than as "immigrants".
We could also make it part of our law that if you illegally/irregularly enter the country you are simply classified as an "undocumented tourists", issued a 2 day tourist visa (which makes you a legal tourist), and directed to depart the country immediately.
In the meantime you are given temporary quarters and meals ~ and not turned loose!
It think that also eliminates any appellate rights any of these guys might have if classified otherwise.
Remember, if the law is to mean anything then we must stretch it to fit circumstances.
Finally! Some one using their head.