Ok, so then you have two choices here:
1. Try and kick all of the illegals out...good luck there...cuz we've been trying to do that for 40 years or more with great success. We'd have to raise taxes, cut spending on other programs to increase the size of ICE and that's no guarantee that it will work.
2. Fine the sh*t out of the companies who hire them in the first place. You know...enforce the laws already on the books instead of legislating new ones (wow..does that argument sound familiar to gun rights fans?). No slaps on the wrist here..make it hurt. Make it so that they won't think twice about not hiring an undocumented worker.
Our thought process has to change when it comes to immigration policy. Its not a dem vs republican thing either. Remember, the all hallowed Ronald Reagan started the whole amnesty thing back in 1986 by signing the Immigration Reform and Control Act of 1986 into law.