The Arizona law doesn't actually infringe on the rights of the affected class, though. All it does is add an additional directive to law enforcement officers directing them to check the IDs of people they have "reasonable cause" to do so with. There are only 2 real problems there.
1: Regular beat cops are not INS agents. They are not the "first line of defense" against illegal immigrants, and making immigration their job means assigning a duty intended for federal officers to carry out.
2: "Reasonable Cause" probably turns into "is this person brown" when you're talking about a state with a border on Mexico, which essentially means this law is a directive telling officers to racially profile. While I'm sure that these officers don't need to be told to do so (being a cop in a border state probably brings with it a certain level of, shall we say... racial tension), it brings up a question of whether or not the law is directed at a specific race. Obviously the law is directed at a minority (illegal immigrants), but a minority defined by being members of a common group known as "lawbreakers" grants them no extra rights. In this case, however, it's incredibly likely that this law would negatively impact citizens far more than it would impact illegal immigrants.
However, this is a debate for another thread.
EDIT: Let me just make clear that this post is not meant to be an endorsement of the Arizona law. I feel that it is both racist AND incredibly ineffective. Illegal immigrants will do their thing, ID or no ID. They might be marginally hindered by a law like this, but it's definitely not getting the job done.