Well, from the Ellis Island web site (funny enough, while looking for information on my grandfather who served on the Mexico border since he served in the New York National Guard at the time), I find this fascinating statement of federal-state roles on this hot button issue:
Prior to 1890, the individual states (rather than the Federal government) regulated immigration into the United States.
Fancy that. For 114 years, states regulated immigration (longer if you count the colonies, I suppose, since they probably just continued doing what they always did after independence). For the last 122 years, the federal government has regulated immigration. Yet Arizona was intruding on a clear federal job.
Just so we remember what the division of labor really has been.
UPDATE: Thanks to Pseudo-Polymath for the link.