On Monday, the Supreme Court handed down its decision in Arizona v. United States, upholding part of Senate Bill 1070 and striking down other parts. Last year, a previous Arizona law on immigration was also before the Supreme Court and was upheld in Chamber of Commerce v. Whiting. With both of these decisions now in the books, its possible to combine them to figure out what the rules are for state laws on immigration.
First, immigration is primarily a federal issue. Any solution to any problems with the current system for deciding who gets to come to the US, who gets to stay once they get here, and who gets sent back will be made at the national level.
Second, state laws on immigration will only be permitted if the state can point to some provision in federal law that supports the claim that the federal government has opted to permit the state to supplement federal immigration law. Last year, the Supreme Court found that federal law expressly permitted states to sanction employers who hired illegal immigrants by sanctioning licenses, and thus Arizona was free to revoke the license to do business in Arizona of any business that employed illegal immigrants. This year, federal law permits local law enforcement to contact the federal government to check immigration status of detainees, so Arizona is free to require its local law enforcement to do so.
On the opposite side of the coin, if the state tries to impose a penalty that is not permitted by federal law, that law is preempted and will be struck down. So no state fines on illegal immigrants for having a job or for being an illegal immigrant. Likewise, a state can't arrest an immigrant for being deportable in a circumstance in which a federal immigrations officer could not arrest the immigrant.
Third, the Supreme Court really did not make a decision on the validity of Section 2(B) -- the "papers please" provision. The Supreme Court rejected an argument that the provision was preempted solely because it might impose an additional workload on federal officials. Because the Administration's sole challenge was the issue of pre-emption (which was the only challenge that the Administration really had standing to make), the Supreme Court did not directly address the other potential challenges.
The Supreme Court, however, did give hints about how it would view a future challenge, and those hints were not good for Arizona. In a two-page segment, the Supreme Court suggested that the statute needed to be narrowly interpreted and that it would not authorize extending a detention beyond the period authorized by other purposes -- i.e. investigating the underlying offense and writing a ticket or, if arrested, holding until bond is posted. As the state courts have not yet interpreted and applied Section 2(B), the Supreme Court held that challenges based on speculation about how it will ultimately be interpreted by Arizona courts are premature.