"Many of those illegals were "guest workers" brought in by the Roosevelt administration during WW2 who refused to leave."
...and that proves what in this day and age, when we have much more control over legal workers ?
Would they try and stay illegally if we ever decide to kick them out again ? ... Obviously, but will will have much more of a paperwork trail, and we might even have a hold over them by making the law so that we can legally withhold SS payments if they don't leave when their time is up.
The best mechanism for maintaining immigration is through the legal system as we currently have in place, which means no illegal immigration, no guest workers, and full enforcement against visa overstayers and sham asylum cases.