Good points all around....
I propose a hybrid.
1. Build the wall (yes, expensive but I'm sure a fraction of just the daily cost of operations in say Iraq...to put it in perspective).
2. Give the border patrol the equipment/people/authority to do their job. UAVs, more personnel, etc. Maybe even have Guard units augment.
3. Institute reformed legal immigration rules.
4. Institute a national ID. Yes, I know all the conspiracy theories, and I'm a libertarian...I know the arguments. In my opinion it is a necessary program in our day in age. A general database of who is who. Nothing more. I don't have a problem with that, as long as it doesnt track anything else.
I think it's unrealistic to think we can round up and kick out so many people from our country. Like it or not they are an important part of our economy and society. Yes, our society too. There will be so many 'humanity' cases if we were to round them up and get them out, it would make our heads spin. Which leads me to:
5. Once our borders are 'secure', our immigration policy more realistic, amnesty everyone...start all over. The illegals become legal, we collect taxes on their labor, all the gray areas disappear. We can absorb those numbers, we already have them.
All these factors combined should allow us to more effeciently control immigration, legal or otherwise.
Securing our borders, being able to quickly and accurately distingush citizens and non-citizens, along with a strong and realistic policy/law to me are absoloute musts for anything to work.
EDIT: I had two number 4's...