I think Matt Yglesias makes a pretty good political point here about trade policy:
If you convince people that it’s not possible for monetary authorities to boost employment, and that it’s unwise to use fiscal policy to boost employment, then it starts to look irresponsible for politicians not to use trade restrictions to protect the jobs of people in their state/district. When an economy is near full employment you can say trade makes the pie bigger and people who lose their jobs will get new jobs. But [if] we’re years away from full employment — which both the Fed and the White House seem to think — then getting laid-off is catastrophic.
The Fed is obviously more concerned about inflation than it is about unemployment right now, and Congress likewise seems unwilling to do very much more to help create jobs. In an environment like that, public pressure for trade restrictions becomes hard to resist. So if free traders really want to keep protectionist sentiment tamped down, they'd be well advised to start supporting domestic policies that create jobs, bring down unemployment, and reduce the kind of financial fear that drives protectonist sentiment in the first place.