Mathematica Policy Research is at the tail end of a non-experimental econometric evaluation of TAA on behalf of the U.S. Department of Labor, but my guess is that the results will become public just a bit too late to influence this round of the policy discussion. The design of the non-experimental evaluation is about the best one can do given the nature of the program and the available data, and will provide valuable information about the program when it is released, but it is by no means ideal.
My thought is that the red team should make the following deal: reauthorize TAA for another five years at roughly the same budget level, but demand that, say, $40 million of the budget be devoted a serious experimental evaluation of TAA and another $10 million should be devoted to the not unrelated task of improving the administrative data systems associated with the program. Then, next time TAA bubbles up to the top of the policy agenda, there will be really compelling evidence available to guide those rare (but not nonexistent) congresscritters at the margin who actually pay attention to such things.
Full disclosure: I am a consultant to MPR on the TAA evaluation.