Anthony, your comments illustrate the imperative that the anti-immigration nationalists see in defining immigration as an "invasion." As nationalism and militarism go hand and hand, they are at home defining every problem as a military problem, just as when Pat Buchanan was claiming that trade barriers must be erected against foreign food and manufactures in the name of "national security." The consumers/private citizens de damned, of course.
Looking at the history of the "uniform rule of naturalization" clause, in that deeply flawed document known as the Constituion of 1787, it is interesting how the federal government immediately began to abuse what limited power this clause grants. Note here that the feds invented for themselves a power of expatriation in which certain undesirables (as defined by the state) could have their citizenship revoked (including those who refused to fight in the state's wars). Yet, I still see nothing about national ID cards or Homeland Security, or coercing employers into performing detective work on their employees, or even anything about border patrol. No such power is even implied by one sentence granting a "rule of naturalization" but as always, the state arrogates to itself every power possible. The Alien and Sedition acts are also a good illustration of early abuses of the clause. Naturally, as many wise men noted at the time, the Constitution of 1777 would have been far less prone to such authoritarian abuses.
Anthony noted the central paradox in all of this:
If the problem with immigration originates with the state, there is a paradox and danger in calling on the state to fix the problem it has caused. There is no knowing what the state will do in order to fix it. There is no guarantee that it will do a good job. It is more than likely that it will make things worse, all while expanding itself and eroding our liberties.
Fundamentally, though, we should keep in mind that even if something is prohibited to the feds, this doesn't mean the states should do it. States can abuse rights almost as well as the feds, and natural law remains inviolable regardless of what any parchment says.