There are so many reasons the new Arizona anti-foreigner law is unconstitutional, but let's start with the Supremacy Clause of the United States Constitution.
“The Federal Government has broad constitutional powers in determining what aliens shall be admitted to the United States, the period they may remain, regulation of their conduct before naturalization, and the terms and conditions of their naturalization. Under the Constitution the states are granted no such powers; they can neither add to nor take from the conditions lawfully imposed by Congress upon admission, naturalization and residence of aliens in the United States or the several states. State laws which impose discriminatory burdens upon the entrance or residence of aliens lawfully within the United States conflict with this constitutionally derived federal power to regulate immigration, and have accordingly been held invalid." (Takahashi v. Fish & Game Com'n (1948) 334 U.S. 410, 419.)
These powers arise from Article I section 8, cls 3 and 4, and restrict the powers of the states under the Supremacy Clause:
“This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.” (Art. VI, cl. 2.)
In other words, whether Arizona believes the United States is not enforcing immigrations laws so as to satisfy the state, it does not have the power to make its own laws. Period.