Need for excess savings
To avoid an impractical "sudden death" cutoff at some income level (say $200,000) tax preferences would need to have a phase in. This would add to the cost and require identifying high-income tax preferences worth more than needed to eliminate the TPC's claimed $86 billion shortfall.
The point is conceded by Romney backer Martin Feldstein (Professor of Economics, Harvard University) who estimates the cost of such a phase-in at $15 billion.
In the article cited below Barro makes a further point - that given the amount of tax preference savings that would need to be extracted from the wealthy to fund the marginal rate cuts there would be little scope to pick and choose - virtually every option would need to be taken. This undermines the rationale for Romney not stating which concessions would go when he said:
I'm going to work together with Congress to say, OK, what are the various ways we could bring down deductions, for instance?. . . . There are alternatives to accomplish the objective I have, which is to bring down rates, broaden the base, simplify the code and create incentives for growth.