Have you ever noticed that Canada doesn't have an illegal problem? That's because their immigration rate is 80% higher than the US.
They also have a guestworker program, and they're a lot farther away from Mexico than we are. As far as the U.S. goes, if we cannot adequately check the backgrounds of the current 900,000 legals per year coming in, what makes you think we can handle another 720,000 immigrants or do adequate background checks for a guestworker program, if we decide we want such a thing?