Here is a repost I submitted earlier to clarify.
My solution would be to first get complete physical control of the border. Not just a border wall, but elevated security cameras and C^3 (i.e. Command Control and Communication). Installation of Pain Beam Systems to deter any attempts to circumvent the border security. This is something we were looking into in the not too distant past (look up pain beam). Remain in Mexico policy. Seismic detectors to prevent tunneling. Reduction in the level of LEGAL immigration to the extent the Dept of State can exhibit the ability to monitor and track each and every legal visa holder's whereabouts (by whatever means the DOS can devise) in the event they attempt to overstay their visas. For instance start off with only 1000 immigrants and see if the State Dept can track every one of them and deport any who attempt to overstay their visa. If they are successful increase it to 10,000 until you determine the State Dept incapable of securing infiltrators.