Regarding the 14th Amendment problem, illegal aliens are not “subject to the jurisdiction” of the United States, in my opinion. They presumably are subject to the jurisdiction of their countries of origin, unless you want to count our interactions with them in law enforcement or the simple fact that they are geographically inside our borders.
If the Mexican Ambassador to the United States gets drunk and runs you over, he can't be arrested for drunk driving. That's because he is not “subject to the jurisdiction” of the United States. In order for him to be prosecuted in the US, the Mexican government would first have to waive his diplomatic immunity. Also, because he is not subject to US jurisdiction, any kid his wife has while in the US is not a US citizen.
Now, if a wetback gets drunk and runs you over, they can and should throw the book at him. They should because he ran you over, obviously. And they can, but only because he's subject to US jurisdiction. Unfortunately, however, that has the well known anchor baby side effect — any kids his woman drops are automatically US citizens because they were born in the US and were subject to US jurisdicition, just as the 14th prescribes.
These congress critters are wasting their time. They need to be working on an amendment to define citizenship appropriately.