What if the U.S. partnered with the E.U.?

What if the U.S. partnered with the E.U.?
Intelligence Squared U.S. Debates - Kaufman Center
If we value a free market in goods and free movement of capital, should we embrace the free movement of labor? Reciprocal treaties would allow citizens of the U.S. and other countries to work legally across borders. Would the elimination of barriers in the labor market depress wages and flood the marketplace with workers? Or would the benefits of a flexible labor supply be a boon to our economy, all while raising the standard of living for anyone willing to work?