Of course, you're perfectly correct - LEOs just can't walk around demanding to see the ID of anyone they choose. The key here is probable cause: loitering (it's why picket lines walk in circles), broken taillights, jaywalking; ya know, the whole Guiliani 'broken windows' approach to petty infractions/crime.
In this case, someone minding their own business working in the fields would not constitute probable cause. A more effective approach would be to investigate employers to see if they were following mandated I-9 verfication processes.
It probably isn't reasonable to round up and deport 11-12 million people and we don't want to live in a police state, but we should at least determine the citizenship of everybody who runs afoul of the law.
I also got ask what we do with the percentage of the 11-12 million who don't qualify for legal status?