Its a politcally untenable position on both sides sadly in the US. If employers were fined 2x, 3x, 4x salary for every single employee found to be working under the table the issue would solve itself. But democrats are of the position that people over staying their visas, illegally immigrating, are as an entire group people who will be killed if they go home so will do nothing to actually make life more difficult for people who do those things. Pro business republicans are happy to allow their constituents to get a leg up in their businesses off the back of immigrants before they deport them so the immigrants can't use any public services.

Yeah, I doubt it'll be solved anytime soon, given how Democrats see it as a way to gain future votes, and corporate Republicans use it to privatize gains and socialize costs. Paying someone under minimum wage while they collect far more in government services than they pay in taxes is a classic example of abusing unpriced externalities.

Republican businesses owners like trump love illegal immigrant labor because it's another thing they can hang over their head. If they start organizing or complaining they can just anonymously tip ICE about the workers and suddenly their problem is solved.

When they say they want to punish immigration they mean punish immigrants.