That's not true - if it were, I don't think the case would be particularly compelling.
First of all, the notion that the Supremacy Clause prevents states from passing laws that deal with issues already dealt with by the federal government is flatly wrong. The clause merely (and logically) states that laws enacted by the states (etc) cannot conflict with the US Constitution or federal law........That is, of course, in regards to illegality
as such. As the DOJ notes, the AZ law does create "
a series of state immigration crimes." This the DOJ objects to, and does claim here that the federal government has a "constitutionally reserved" right to handle immigration, although I was unable to find a believable justification for that claim.
NONETHELESS, the DOJ does have a strong case to make, if you read their
brief.
.....The main crux of the argument is that the AZ law overreaches....
DOJ is making the argument that the AZ law will undermine federal immigration policy. As absurd as that may sound, the basic argument is that INS and ICE's limited resources will be excessively drawn to cater to minor immigration problems exposed by the AZ law at the expense of higher priority (national security) cases and the government's intended policy on immigration (the quality of that policy not being particularly relevant).