Good point. A quick check of Article I Section 8 only speaks of Naturalization. Immigration would then fall under the 10th Amendment. I do stand corrected.
If it were this easy, Arizona, California, Nevada, Texas should be able to put up their own border fences.
I can see the Solicitor General arguing to the court that even though the SCOTUS has earlier judged that border protection belonged to the federales, they really don't want to do what's necessary because of cost, too much traffic, indolence, etc.
That might well break even Sotomayor!
Arizona has not yet gone to the point of protecting its own borders, but as long as such protection didn't violate interstate commerce I suppose they could do it. In fact, "the people" could do so.