Again, the LOCATION is key here.
As I said, the feds have authority over the border and who crosses. But the feds generally do not have authority over what is within the State borders.
Once the illegal crossing is made, it generally is up to the states to deal with it. But in this case, the feds have screwed up so badly that they should at least help round up the illegals but under and with State cooperation.
The States are generally constitutionally sovereign against federal interference.
The law does not support that claim. "La Migra" is well within its authority to raid suspected illegal immigrant employers anywhere, any time.