Play stupid games, win stupid prizes!
I have a novel idea for people that do this. If they're American Citizens, permanently ban them from any sort of social welfare. No unemployment, no disability, no social security, nothing, oh and for good measure, no voting rights. Oh, but they still have to pay taxes, they just don't get the welfare benefits. And if they choose to emigrate from the US, they have to pay the next year's taxes in advance before they can leave. I call it a "Divorce Bill."
If they're not citizens, shoot them as human smugglers. We need to take more drastic approaches to these foreign invaders.
I propose a two strike system. Get caught entering the country illegally? Deported and permanently disqualified from asylum and legal immigration. Effectively banned from the US. Try again and we reserve the right to execute you as punishment. To Hell with the Geneva Convention. American Law should only apply to American Citizens. Foreigners and non-citizens should not get the same legal protections. They shouldn't get any to be honest.