Yes, but they can delegate it to local authorities if they choose...and just this past week, they DID choose. Seems Florida local authorities now have the authority to arrest your precious illegal aliens.
By the way, You did not post this yesterday (at least not on this thread).
Thats a federal law that enlists state law enforcement in apprehending those in violation of federal law. Try again HEEROO. The regulation in matters of immigration and naturalization is strictly a power of the federal government.
In making Immigration laws, yes, but in enforcing immigration laws, no.
Your argument was the enforcement of immigration laws. There is nothing in the US Constitution that prohibits the States from enforcing immigration laws. The states could close down their borders with Mexico and Canada if they wanted to, the protection of the state border is in the hands of the states.
For the purpose of this section the jurisdiction of such State and local officers and of the State and local courts shall extend over such immigrant station.
This code of law, gives the States the power to shut down any Port of Entry they want, for what ever State law they wish to enforce.