Well let's see here. If it is a constitutional problem to enforce a federal law on immigration violations then should the local LEO's enforce armed robbery of Federal Banks? Of violations of federal firearm laws? Of using fraudulent passports and other federally issued documents? Of federal possession of federally prohibited explosives or other harmful detonating devices? The list could go on and on if one starts thinking about the many federal laws that the locals already enforce or make arrests for during the course of a routine day. I think you get my point here.
I'm not trying to be flippant but the analogy you proffered isn't unique but one the OBL types like to present as reasons why not to enforce our federal immigration laws and stopping the mass invasion of the law breakers from outside our borders.
I believe, if I'm not mistaken, this was the subject of the Supreme Court case in which it was held that Congress was not authorized to commandeer the executive agents of another sovereign.
Sorry, I have no problem if the local sheriff doesn't enforce federal law. As I read the constitution, there is about a micrometer of area in which Congress can pass criminal law. I am of the opinion that the rest of it is unconstitutional.
As I said before--if Congress wants to pass the law, then let's see them enforce it.