You can't have it both ways. Regardless of how this issue is settled, it is going to require more government action. Wishing won't make illegal aliens disappear; it will either take massive law enforcement for arrests and deportation or more people to keep track of those who become legal through this plan. Ther is no small government solution.
I think big government is a big part of the problem. For example hiring an illegal costs $100 / day for however many days you need them. Hiring a citizen requires unemployment and withholding taxes paid in cash to the government. Although you get to deduct the legal employee costs, it increases your chances of audit. The jobs that these people get helps them assimilate but they aren't paying their way when they are paid in cash. The massive government you are talking about will have to be paid for by the rest of us.