If you really wanted to toss this into a mess...agree to a pathway to citizenship...for what is projected to be only eleven million, and limit it to precisely that number. The longer in country...the higher the odds you get accepted, but you have to prove that fact. The guys after 11 million? They get a 100-day pass, and then need to leave the country. Anyone hiring those folks....goes to jail....real jail (nothing less than 30 days for anyone who hires illegals with the new deal).
Do you think you are going to put a bridle on Rats? Every compromise just leads to the next.