I think you're right about Minimum Wage Laws practically forcing small business to hire illegals.
Here's another problem:
Big difficulty for humanitarian church groups: how can you tell whether a particular homeless, hungry, or sick person is a citizen or not? For that matter, how can an employer tell whether a job-seeker is a citizen or not, given the ubiquity of fake Social Security numbers and other forms of false identification?
Looks like we'd have to have some kind of forgery-proof universal I.D. system (using computerized iris-scans? fingerprints?) covering every person in this country without exception.
Are we willing to go along with that?
(If I'm wrong about this --- I'd LOVE to be wrong about this --- so don't just call me a dork. Explain why.)
A huge increase in laws and enforcement of those laws will be required to ensure that humanitarian (including church) groups don't give aid to illegals or they will be prosecuted.
I don't agree that more bureaucracy is the answer.