After reading your post, I can only conclude that your not a Libertarian. In fact, I have no real disagreements with your positions. Although, I would add a few points.
There are other problems besides public acceptance for treating immigrants differently than natural born citizens. First and foremost, I doubt they would survive a legal challenge on equal protection grounds.
I agree, particularly in the light of the expansive view of the 14th amendment seen in recent Court decisions.