The illegals are very much law breakers because they are in this country illegally. Don't try to paper it over by saying that's the way it is everywhere else.
"We the people have to deal with the hand the FedGov dealt us, and that means the States are stuck with it."
We the people don't have to do any such thing. In case you've forgotten, or perhaps went to public school, the government works for us. The states are only stuck with it to the extent we refuse to insist the federal government enforce our immigration laws. You seem to feel this is too much to ask.
Your comments indicate a very large gap in your understanding of the illegal alien problem. To catch up, you need to do a lot of homework.
Gummint is riding a tiger now. Gummint, huge though it is, does not have the resources anymore to deal with the tiger and can only hope to not get thrown off. I appreciate your suggestions for further education and am already expanding my reading list. I won't bore you with suggestions of my own since I do not know the extent of your personal library of appropriate reading.