Alan Greenspan seems to think relaxing rules on immigration will help America. I think this is short-sighted.
If it's about keeping down wage costs, remember that low-paid workers also claim on a range of social benefits, and the people they are undercutting even more so. The last thing a country needs is a hereditary class of long-term unemployed.
If it's about skill shortages, highly-skilled foreign workers are getting harder to find: as emerging economies develop, they want the same people. My brother in America notes that over the years, his university has attracted fewer foreign mathematicians for this reason.
The quick-fix approach is not a lasting solution. Like the UK, America needs to improve education and vocational training. If times get tough and foreign workers go home, the USA's dependence on them could result in economic "cold turkey".