The strongest part of Barro's analysis is the conclusion:
Finally, I would note one item that the Romney campaign does not cite in support of its tax plan: Any analysis actually prepared for the campaign in preparation for announcing the plan in February. You would expect that, in advance of announcing a tax plan, the campaign would commission an analysis to make sure that all of its planks can coexist. Releasing that analysis now would be to the campaign's advantage, helping them put down claims like mine that their math doesn't add up.
Why don't they release that analysis? My guess is because the analysis doesn't exist, and the 20 percent rate cut figure was plucked out of thin air for political reasons without regard to whether it was feasible.