Governor Pawlenty was getting too moderate lately, so it was time to prance back towards the conservative end of things. He did this by demanding that police be able to act like INS agents
by asking people about their immigrant status. This despite the fact that most law enforcement agents do not want this.
Unless you are familiar with the INS, it may not be clear why. People who have not dealt with the INS or known somebody who has have absolutely no idea how arbitrary, illogical, and bureaucratic the INS can be (actually, it's not even called the INS anymore). It is probably as close to living in the former Soviet Union as Americans can get. Field directors hold complete power over their little fiefdoms. Applications sit in boxes in warehouses for years. Service is unavailable to all but those with money. It's probably the worse governmental agency out there, even worse than the IRS.
It's therefore not very easy for many people who are non-citizens and in the clutches of the INS to be able to give a short answer to questions about whether they are legal. Sometimes, in order to become a legal immigrant, you have to be illegal for a while. Sometimes it doesn't matter what you do. People hire lawyers to figure these things out, and the rules and regulations change so quickly that even lawyers and the INS agents themselves don't know what is going on. Injecting police officers into this mix, who will be completely unable to follow any of this, is a bad idea.
This has nothing to do with fighting terrorism. If a criminal is arrested for committing a crime, their immigration status will come out soon enough. However, it sounds like the Governor wants police officers to be able to go up to any dark-skinned person asking suspicious and ask for their green card. That's not law enforcement, that's intimidation.
It's also read meat for his conservative base, the kind of people who rant about "furriners" and are only too happy to shut the doors to this country. Don't count me in as a supporter of that mindset.