How about starting with securing the borders? Fining employers who hire illegals when they are found. It sounds like you're implying there is nothing that can be done to take away the "benefits" of coming illegally to America. Currently the benefits outweigh the slap on the wrist and free ride back to the south american shithole they came from. That needs to change.
Unfortunately there's really not a way to secure the borders 100%. It's not hard to accidentally drive into Canada if you're in northern VT, NH or Maine (my parents did it while beagling from VT into QC). The border with Mexico is more rural and much bigger than VT and Quebec. Plus we have a huge amount of ocean coastline from Texas to Maine and CA to Alaska. Chinese get smuggled in by shipping containers.
Plus, if we do a real hard push to secure borders, it'll jack up taxes, will tick off the anti-LEO crowd (including many here) and will probably violate someone's 4A rights, or maybe 2A rights.
If we just shoot on sight, that won't go over well internationally.
I have worked in places with illegals and the only way I can think of keeping them out of our businesses is to inspect every potential business (manufacturing, janitors, landscaping, etc.) at random, unannounced times. But then inspectors can be bribed and someone will claim this is an infringement on the rights of the business owner.