Yes, there should be a restriction, but it would put a real hurt on farmers, ranchers, and other industries who need unskilled labor. We know that most of our own unemployed would never even consider taking a job like harvesting crops or digging ditches. And why should they when the entitlement train is so easy to climb aboard?
Our government is well aware that most of the unskilled jobs are filled by those who are in this country illegally. Perhaps that is why they pay so little attention to our open borders? If they truly closed the borders we would have crops rotting in the fields and an apple would cost $10 at the supermarket.
I would say that if these unskilled jobs were taken by our own citizens there should be restrictions. But until that happens it would be those who grow our food who would suffer along with we consumers of these products.
And finally, they don't really enforce the immigration laws we have now so would new laws make any difference? My guess is no, nothing would change.
Great question by the way.