U.S. Constitution, Article 1, Section 10: Powers Prohibited of States:
No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts; pass any Bill of Attainder, ex post facto Law, or Law impairing the Obligation of Contracts, or grant any Title of Nobility.No State shall, without the Consent of the Congress, lay any Imposts or Duties on Imports or Exports, except what may be absolutely necessary for executing it’s inspection Laws: and the net Produce of all Duties and Imposts, laid by any State on Imports or Exports, shall be for the Use of the Treasury of the United States; and all such Laws shall be subject to the Revision and Controul of the Congress.
No State shall, without the Consent of Congress, lay any duty of Tonnage, keep Troops, or Ships of War in time of Peace, enter into any Agreement or Compact with another State, or with a foreign Power, or engage in War, unless actually invaded, or in such imminent Danger as will not admit of delay.
Article 1, Section 8: Powers of Congress:
To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
There’s a whole slew of other powers granted in Section 8. The power to lay and collect taxes. The power to establish post roads. The power to establish Tribunals inferior to the Supreme Court. Organizing the militia. These are all things allowed to both the Feds and the States. You know why? Not prohibited to the states in Section 10.
The uniform rules of naturalization is not in jeopardy here. Arizona isn’t trying to come up with its own rules on who is or isn’t a citizen. It is simply prohibiting non-citizens who have failed to properly enter the country from traveling freely there. (That is, by the way, directly in line with the Federal laws.)
And of course, there is Article 4, Section 4:
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
Emphasis mine. There is certainly a constitutional problem here. Arizona ain’t it.