Bill,
Within a hundred miles of the border its legal. ICE does not subscribe to the requirement that they need reasonable suspicion. It's not right, but we have ceded so much power to the Federal government in the area of immigration and customs enforcement we'll never get it back to a balance between citizen's rights and government intrusion. It is clearly tilted in favor of the government IMHO.
In the areas where they patrol or run roadblocks, ICE Agents can stop anyone, and assess whether they are in this country legally. If you choose not to cooperate, you likely will find yourself in handcuffs or worse.
http://www.youtube.com/watch?v=YUzd7G875Hc