Here is an interesting interview by Fox News. Francisco Hernandez, a lawyer from Fort Worth, Texas, essentially says that a sheriff is not restricted by local laws from reporting illegal aliens to the federal government. Essentially, federal law supersedes local laws. So, if law enforcement is serious about this issue, then the only push back they are experiencing is political.
My understanding is that the chief law enforcement officer in the county is the sheriff. That is the main official to whom people look for protection in their county. Please see the clip of this interview attached below.