In particular, the workhorse theory of International Trade, the Hecksher-Ohlin Theorem, leads to the Stolper-Samuleson Theorem, which shows that when countries start trading with each other, the relatively abundant factor of production in each country becomes better off, while the relatively scarce factor becomes worse off. In the US context, this implies that opening up trade will leave capital better off relative to labor, and skilled labor better off relative to unskilled labor.
Does trade increase the total size of economies? Yes--this is something that economists do agree on. But in the absence of redistribution--something that seems to be anathema to we Americans--more open trade will make low skilled laborers worse off.
In my ideal world, we would pass the Trans-Pacific Partnership (TPP), a potential [quasi]-trade agreement among the US and 11 other countries of the Pacific Rim, and redistribute its bounty such that everyone would be better off. There is no evidence that our political system would allow this to happen.
Despite all this, I do and will continue to support trade agreements such as the TPP because that there is some evidence that they prevent wars. Of course, as someone who has had nothing but good fortune in life, it is easy for me to think that the abstract prevention of war is more important than the tangible reduction in other people's already low wages.