Forget E-verify.
Change the law. Make it a felony to be in the US illegally
Give them 90 days to get their affairs in order and leave the US with their anchor babies in tow. If you are caught in the US after that 90 days or 180 days you will be deported and prohibited from ever entering the US again, legally or otherwise. If you are found here illegally again, is a capital crime.
You militarize the border with 100,000 troops. Tijuana to Matamoros. Orders are: shoot to kill anyone or anything headed north. Create clear lanes for those headed south.
We are both ultra-right-wingers I have no doubt. But the steps have to be palatable to the general public. What could be more fair and easy than simply trusting but e-verifying?
Give them 90 days to get out... Then give employers 90 days to replace them or THEY go to jail for having illegals. No e-verify confirmation? Your charged.
Lot fewer employers to deal with than illegal invaders. Dry the job supply up and cut off the welfare for flunking e-verify and they will go home.