There is no way that they find this law unconstitutional. Article VI of the same Constitution you're talking about should shed some light here...
http://topics.law.cornell.edu/constitution/articlevi
Seeing as "Aliens and Nationality - 8 USC Title 8" (http://law.onecle.com/uscode/8/index.html) and more specifically "8 USC Section 1304" (http://law.onecle.com/uscode/8/1304.html) is federal law, and has been since 1940, it is "a law of the United States... made in pursuance [of the Constitution], under the authority of the United States, [and is] the supreme law of the land," so designated by the same Constitution that you bring up so frequently.
So, as seen in this case, the AZ law overlaps an already existing, longstnading federal law which is considered, by that same Constitution, the "supreme law of the land." Therefore, there is no basis for a challenge on the grounds of constitutionality, as any state law that overlaps a federal law is, by default, constitutionally sound.
You're refuting this based on a wrongheaded premise (not unlike most of those who don't see the problem).
The first thing you're wrong on is believing states have the right to pass laws which attempt to mirror federal law. They don't specifically with matters of state...which immigration is one. For example, even if the US has a treaty with Comoros or something..it would be unconstitutional for a state to enter into it's own treaty with Comoros.
The law provides that everyone in the country is presumed to be here legally. SB 1070 gives no guidance for what constitutes a reasonable suspicion or probable cause for compelling an individual to demonstrate their legal status.
Further, it makes permissible detention (unreasonable search and seizure) based on not performing a task you have the right against performing.
The supreme court has ruled that it is permissible for law enforcement to ask you for your identity (not produce it). In fact, law enforcement may ask you whatever they want. You don't have to answer anything beyond telling them your identity though. But when AZ makes the standard probable cause someone is here illegally...what is that and how is that determined without first violating someones right against an unreasonable search and seizure???
Every person here is to be presumed here legally.