The priorities for the immigration enforcement activities are those who pose a risk to national security, so your terrorist types. Next come those involved in organized crimes, crimes against humanity, and criminals. Once we've looked after those people, we go after failed refugee claimants, and then all others--those who overstay, and those who work, study, or misrepresent themselves, including marriages of convenience--are our lowest priority.
On March 10th, 2008. See this statement in context.