Actually, the USC gives sworn state and local officers the authority to enforce many federal laws, including most of the criminal laws.
Most local LE agencies have policies in place against using immigration laws as the sole basis for detention, arrest or investigation. This is a matter of political pressure and is wrong in some respects. It is also changing rapidly in the wake of 9-11. The feds are also getting smarter about how they do it. For example, while local policies may forbid arresting somebody for immigration violations, the feds have started getting warrants for immigration violators and entering them into the computer. Local officers are usually bound by state law to serve warrants, so it gives them a convenient "out" and a way to enforce the law without running afoul of the political aspects.