Worried about cheaters?
Then go after the employers.
I can't blame anyone who crosses the border because they want to work. They have families to feed too.
I have problems with people who tempt undocumented workers by offering jobs, knowing their prospective employees are probably illegals, and often pay them far less than a citizen or legal immigrant would receive for the same work.
It's easy to take out your anger on the people with the least power and the most to lose. They're easier to punish, I guess. The employers have lawyers and assets, paid for by all the money they made by hiring people they lured here.