THE CASE THAT Republican presidential nominee Mitt Romney will make to the American people Thursday evening and in the ensuing campaign will rest heavily on his promise to reduce taxes. Mr. Romney, a former Massachusetts governor, has said that he can do so without reducing revenue and increasing the federal debt. We’ve asked him to show his math. Now comes, ironically from one of his advisers, further evidence that Americans ought to demand a more detailed explanation.

Mr. Romney says he can work his magic by “broadening the base” — increasing the amount of income that is subject to tax by getting rid of loopholes. This sounds great in principle; it’s a matter of “getting rid of a lot of the underbrush” in the tax code, Sen. Rob Portman (R-Ohio) said Tuesday. But the really big loopholes aren’t oil-depletion allowances and the like; they’re tax deductions that millions of Americans have come to view as entitlements, such as for mortgage interest and charitable giving. The Tax Policy Center (TPC), a nonpartisan joint venture of the Brookings Institution and the Urban Institute, recently analyzed Mr. Romney’s proposals and found that there would be no way to implement them without raising taxes on the middle class.

In an op-ed in the Wall Street Journal on Wednesday, Martin Feldstein, a leading Republican economist and a Romney adviser, took issue with the TPC’s conclusion — but with calculations that, in our view, bolster the case for Mr. Romney being more forthcoming. Mr. Feldstein says that the Romney income-tax rate reduction, and a couple of other tax changes he favors, could be paid for by eliminating all deductions for taxpayers with adjusted gross incomes above $100,000. Since the top 21 percent of taxpayers are in this group, Mr. Feldstein argues, it proves that the TPC is wrong.

The economists will argue over some of Mr. Feldstein’s assumptions, and he acknowledges that his plan doesn’t pay for the estate tax elimination that Mr. Romney also favors. But the bigger points are these. Even if you accept Mr. Feldstein’s definition of middle class as those earning less than $100,000 — and we think quite a few Romney voters might object — it remains true that in his hypothetical version of the Romney plan, people making between $100,000 and $200,000 would end up paying more in taxes. Millionaires would end up, on average, paying a lot less. The thrust of the TPC conclusion about who benefits seems to us to hold true.

And would taxpayers now deducting their state income taxes, church donations and mortgage interest view those benefits as “underbrush?” Would they trade every dollar of those “loopholes” for a simpler tax code, even if it meant a higher tax bill for them? Maybe they would. But we think that they ought to understand the choices before they vote, not after.

Mr. Feldstein, in his own capacity, favors a different plan — keeping all deductions but capping the total amount that anyone can deduct. We think there’s sense in that, but of course it wouldn’t pay for as big a rate reduction as Mr. Romney is promising. What’s Mr. Romney’s view? What’s his plan? He is very specific on the rate reduction. Let’s hear how he would pay for it — and who would pay.