One problem is that the US does not know who should be in the US as a citizen; there is no list of citizens.
Maybe what is needed would be a RFID chip implanted at birth in every child born in the US and in every current person in the US who is registered to vote as well as every Naturalized US Citizen. A RFID chip could be read remotely just like credit cards and only those who have the chip could buy, sell or vote. Anyone without a RFID chip could then be easily identified when they pass near a scanner in all public places, rounded up and then either sent to the Citizenship school where if they pass the tests to become a citizen get their RFID implant or should hey fail get deported.
That certainly should appeal to the vast American Base since it serves multiple purposes; identifies who should be here and hurries along the END TIMES party.
Problem is, once the RFID chip is hacked by the Russians, we may all be doing Putin's bidding. Or maybe that is the end game.
Kidding aside, one thing I have always considered when it comes to illegal immigration is focusing on the root cause. These people are often leaving areas that are in dire straits or very violent. A simple solution I always considered from my perspective that will help ameliorate part of the problem is end the idiotic drug war.
A big issue as it pertains to illegal immigration from countries like Mexico, Columbia, Bolivia and so forth is the fact that they are controlled by various drug cartels. And the government is corrupt and usually in the pocket of the Pablo Escobar types.
The drug war, especially in the USA, is helping to prop up these dictators and criminals. If we decriminalized drugs, it would reduce the power hold many of these people have in their countries. That was a lesson we learned with prohibition. Outlawing alcohol fueled the criminal element and gave rise to people like Al Capone. Once it ended, the crime rate dropped dramatically.