Authority over immigration is federal. This is based on Constitutional powers as interpreted by the Supreme Court: naturalization (Article 1, Section 8, Clause 4), foreign commerce (A1, S8, C3) and sovereignty (various Constitutional principles including the necessary and proper clause [A1, S8, C18]).
There is an inherent sovereign power to regulate international affairs. It breaks legal doctrine and stretches credulity to argue that individual states should have power over international borders.
States can complement national laws, not substitute for them. Utah politicians have suggested various proposals to address undocumented aliens in the state. Some deal with enforcement while others deal with benefits. Federal law would preempt most, if not all, of these proposals.
State action would be costly, misguided and disruptive. Reform must be national. It should flow from good public policy not politics.
Henderson v. Mayor of the City of New York (Sup. Ct. 1875)
State restrictions on immigration infringe the federal power over foreign commerce.
The Chinese Exclusion Case 130 U.S. 581 (1889)
“In December, 1878, the convention which framed the present Constitution of California, being in session, took this subject up and memorialized Congress upon it, setting forth in substance that the presence of Chinese laborers had a baneful effect upon the material interests of the state, and upon public morals; that their immigration was in numbers approaching the character of an Oriental invasion, and was a menace to our civilization; that the discontent from this cause was not confined to any political party, or to any class or nationality, but was well nigh universal; that they retained the habits and customs of their own country, and in fact constituted a Chinese settlement within the state, without any interest in our country or its institutions, and praying Congress to take measures to prevent their further immigration.”
The power of exclusion of foreigners is an incident of sovereignty belonging to the government of the United States (paraphrased).
De Canas v. Bica 424 U.S. 351 (1976)
The power to regulate immigration is unquestionably a federal power though not every state enactment which deals with regulation is preempted by the constitutional power (paraphrased).