The cart you speak of is a guest workers program coupled with a form of amnesty. That doesn't solve the problem. It only perpetuates the problem. I say seal the borders first, prosecute employers who break the law by hiring illegals and halt welfare for illegals. Then we can talk about a guest workers problem that has a chance of functioning properly with longterm success. Amnesty right off the bat, is out of the question.
And I think the carrot has to drop during or just before the stick.