I believe it was Carson in IA stating he preferred a guest worker program but you could only apply for it from outside the US. no exactly how sure that resolves those inside that refuse to leave (so they can apply).
SImple....require government work permit before employers can hire or continue employment. Just like they do in Singapore. Result is there are no illegals working in Singapore. And Singapore knows exactly who is in the country, where they work and where they live.