The constitutionality of this law will be challenged shortly, several parties have already announced their intentions to do just that. Whether they will succeed is another matter. I think that one of the most thorough answers on this question was given by jrperez, yet his/her conclusions seem simplistic. I will address the points:
1. Preemption: There are many instances of local and state law enforcement acting on behalf of the federal government in areas where they have limited jurisdiction, but on the immigration issue itself here are excerpts taken from the National Immigration Forum:
"A published 1996 Justice Department Office of Legal Counsel memo states that local police have the authority to arrest persons only for criminal immigration violations. A 2002 unreleased memo from the same office states that police have the authority to make arrests for criminal and civil violations"
There are more examples, but as it stands state and local law enforcement has been given partial, and sometimes full, authority to detain illegal immigrants. Only explicit action by the federal government can make preemption an issue, in my opinion, and so far nothing has happened to that effect.
2. Equal Protection: if the law does indeed lead to violations of equal protection, then it will be unconstitutional, yet we do not know if this is the case. The first thing we must understand is that more than 30% of Arizona's population is of Latino origin, this means that if "reasonable suspicion" is based on race, then the jails and the police stations will get overwhelmed simply from processing the "suspects." This means that police cannot practically use race as a basis for "reasonable suspicion." So the question really is: what will qualify as "reasonable suspicion" under this law? This question is unanswered, despite what many people are saying about this law leading to racial profiling.
3. Due Process: this does not seem to be violated by this law. What constitutes illegal immigration is clear and those who enter or stay in the United States illegally are well aware of the crime they are committing. This does not seem to be a big problem.
In general, the constitutional problem with this law rests on how the state chooses to define "reasonable suspicion." I do not believe that the state CAN (or should) use race as a factor when determining suspicion, simply on the basis that it would completely overwhelm law enforcement in AZ. Being a Latino living in a city with a large Latino population, I can assure you that it would be disastrous to law enforcement if they choose to adopt a policy of racial profiling, in terms of community relations and trust between citizens and police.
If their basis for "reasonable suspicion" is constitutional then so is the law, in my humble opinion (barring some direct action against it by the federal government).