The Supreme Court voted 5-3 to uphold an Arizona law which in effect shuts down businesses for hiring illegal immigrants. Justice Kagan did not participate, presumably because she had been US Solicitor General during the lower court reviews of the case.
Those opposing the law said it was improper because of federal control over immigration law, but the Congress had included provisions in the legislation they passed which specifically allowed states to regulate licensing.
In the case of the Arizona law, the state would not recind the license fo the business until the 2nd offense and if the employer used the Federal E-Verify program they also would not be punished.
I have not had time to review the rulings in detail but it seems to me that licensing is something the states are empowered to do and the federal law specifically allowed them to do this. In addition we are talking about punishing the employer, not the employee.
The ruling can be read here.