Add some incentive for cooperation from foreign governments.
I read somewhere recently that ICE has to release captured foreign nationals when the nation they came from does not take them back. How about we give those nations some incentive. Lets beginning charging them for the cost. Start by setting aside a significant sum of money, seized from their assets in this country or from foreign aide to be sent to that country. Something along the lines of a million dollars per person. Put into a find for administration, housing, transportation and health care. Keep depleting it by the day (say it costs $500 per day including administrative fees, housing, food, health care, and what have you) and deduct that from the amount to be released when the person is repatriated, that and a couple grand for transport. Double the amount withheld for repeat offenders. Keep half as a penalty to insure increased cooperation from the foreign nationals home land.
Provide disincentive for people to stay
Treat income gotten in this country by people not legally in this country as criminally gotten gains. Confiscate them. Use it to offset the cost of providing care for the poor and displaced that are legally here. People who can't make a living because they are being driven out of work by the influx of foreign nationals. Let local law enforcement or townships keep the money and local enforcement of immigration laws will sky rocket. This isn't discriminatory. Let a citizen use a car in a crime and guess what happens to the car.
Set up a decent guest worker program
A program that would make labor available where it is needed but under very strict regulations. Blood tests, DNA samples, quarterly testing re-certification. A program that will use DNA to insure that people are identifiable, and prevent people who are criminals from getting into or staying in the country. Use a national registry and a workers card that ties every action into that database. Tie the right to stay to gainful employment, no gainful employment and your "legal status ends" which means that the state can confiscate your assets unless you leave. Finally, no guest worker can receive benefits paid for through taxes even though they must pay taxes. That includes Social Security. If you want to come and work do so. But when you aren't working go home. The price you owe the American people who did build this great national economy is the taxes you pay for the benefits you aren't entitled to collect. But of course, for those who remain free of criminal activity and health risks there is a waiting line for the opportunity to become a citizen. Being a guest work does not preclude them from getting in that line, but they get no special consideration because they are here.