Ever since Simpson-Bowles, it's become a mantra in Washington: Lower the rates across the board and close tax loopholes and other expenditures to help broaden the base and pay for the tax cuts.

Mitt Romney himself has placed it in the center of his campaign. "Mitt Romney will pursue a conservative overhaul of the tax system that includes lower and flatter rates on a broader tax base," his campaign's 59-point economic plan says, citing Simpson-Bowles.

In theory, it seems to make a lot of sense. Tax expenditures not only complicate the tax code, they also seem like a significant source of revenue: They are projected to provide more than $1.4 trillion in revenue in 2015 alone, according to the Treasury Department. But there's significantly less potential savings from closing loopholes if you reduce rates first.

(Daniel Acker/Bloomberg)

The problem is, lowering tax rates lowers the return on most of these tax expenditures, as the expenditures themselves are tied to the income tax rate, the Tax Policy Center explains in a new report. "Thus, cutting tax rates reduces the amount of offsetting revenue that cutting tax preferences can raise," the authors write. So it becomes that much harder to close the revenue gap and pay for the across-the-board tax rate cuts.

The Tax Policy Center breaks it down in this chart, which shows what happens to the revenue from tax preferences under: 1) current law (in which the Bush tax cuts expire), 2) current policy (with the Bush tax extended), and 3) Mitt Romney's reduced rates, with a top income tax rate of 28 percent, a 15 percent capital gains rate and a repeal of the AMT:

(Tax Policy Center)

All this means that the political task of coming up with acceptable revenue sources to offset the cost of tax reform is even more onerous than it may appear.