So where does the federal law say the State or localities can't assist in enforcing federal law?
In my opinion, it wasn't a matter of willingness to assist, it was a willingness to go beyond the power the State constitutionally had to enforce immigration law. Section 5(C) of SB 1070, for example, is seen as an obstacle to the regulatory power of the government as put forth in the IRCA of 1986.
The error with Section 6 of SB 1070 is better explained by the Supreme Court itself:
"Section 6 attempts to provide state officers with even greater arrest authority, which they could exercise with no instruction from the Federal Government. This is not the system Congress created. Federal law specifies limited circumstances in which state officers may perform an immigration officer’s functions. This includes instances where the Attorney General has granted that authority in a formal agreement with a state or local government. See, e.g., §1357(g)(1). Although federal law permits state officers to “cooperate with the Attorney General in the identification, apprehension, detention, or removal of aliens not lawfully present in the United States,” §1357(g)(10)(B), this does not encompass the unilateral decision to detain authorized by §6."
--Supreme Court majority opinion, Arizona v. United States, 567 U.S. __ (2012)