You know what guys?
The analogy of the locked door vs. only an alarm system is perfect. I read all of the other responses too. They hit the nail on the head so I am going to concede my original, unfiltered statement

I would rather they be kept out instead of racking up taxpayers' dollars in incarceration and deportation.
A barrier that is quite difficult to cross PLUS the electronic net to spot the most determined jumpers that DO breach it. We still are going to need a much boosted manpower supply, and I believe the armed citizenry can fill a part of this role perfectly.
Shit on the home front will have to be beefed up too if we want near perfect deterrence. Do regular audits and start leveling up the fines of businesses who think they can hire illegals under the books and get away with it. $5000-$10,000 for EACH undocumented worker we discover at your place, and let's see who else want to run the risk. Your choice: Take shortcuts and face financial ruin, or obey the law and be a team/community player.