Brendan Nyhan had an interesting piece in the NYT's Upshot section in which he discussed how "free trade" policies get pushed by presidents and approved by Congress even though most middle income and lower income people are opposed to them. Nyhan refers to research showing that wealthier people overwhelmingly support "free trade," and politicians are likely to act in ways that reflect their views even when this means going against the majority.
While this is interesting and important research, it misses an important part of the story. Our trade agreements have not been about liberalizing trade in all areas, as Nyhan asserts. While trade policy has been quite explicitly designed to put U.S. manufacturing workers in direct competition with low paid workers in the developing world, it has largely left in place or even increased the protections that keep doctors and other highly paid professsionals from other countries from working in the United States.
Trade theory predicts enormous economic gains from allowing freer trade in these professionals, but because trade policy is designed largely by and for wealthy people, removing barriers to foreign professionals working in the United States rarely gets on the agenda in trade deals. Unfortunately it also doesn't get mentioned in the media's discussion of the issue either.
