So this is how the Arizona law would be enforced

Notice that all he did is expound upon the rights that they (police/DHS) are not supposed to have (illegally detaining people without lawful purpose; ie probable cause). This is naturally something that can get you arrested and charged (if police/authorities can invent some charge on which to do so, disorderly conduct is popular for this). But I'm aware of no law or right of police (you are obstructing me from doing my job to the contrary...) that prevents citizens or anyone else from questioning US authorities and refusing to answer their questions on the grounds that they do not need to know the answers to those questions (without establishing probable cause. Indeed, you may still refuse to answer even if they have probable cause....). These are not only hard coded rights of citizens enshrined in the Constitution but they have been spelled out by repeated federal and state court decisions. And yet we are to believe that in Arizona police will not adopt tactics very much like these in order to blur the distinction between legal and lawful contact between police and residents/travelers/immigrants (reasonable suspicion and probable cause) and illegal and unlawful contact, demanding documentation without prior conditions, as at a checkpoint like this (for example a DUI check point could be setup by local police to accomplish very much the same thing).

One other thing: a person should not have to vociferously and repeatedly ask to have their civil rights, in this case their freedom of travel, granted by an authority figure. The games being played here to pester and frighten people, who usually will not be so well versed on court rulings and Constitutional law, into ignoring or surrendering their basic rights, even for petty things like "are you a US citizen?" are somewhat frightening. But it sort of reminds me of the A/V analogy for airport security from here. "This is the overhead projector and nobody can touch it but me!" (around the 6 minute mark)