Does a State Have the Power to Deal with Immigration?

The Cafferty File, part of The Situation Room on CNN, poses a question every hour The Situation Room is on. This is today's 5:00 question, and Thoughts on the World's response.
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In the absence of enforcement of the nation's immigration laws by the federal government, is Oklahoma right to crack down on its own?

Of course Oklahoma has the power to crack down on illegal immigration. Why wouldn’t they? State’s rights and federalism allows each state to have their own powers: education, health care, etc. If they can deal with education, why’s it such a big deal that Oklahoma is dealing with immigration?