The analysis doesn’t include every possible tax expenditure, leaving out, for example, the tax break employers get for providing health insurance. But because Mr. Romney refuses to raise capital gains taxes and wants to end the estate tax, it is hard to see how he could do much better than 4 percent.

This is why Mr. Romney has refused to say which deductions he would eliminate, just as Representative Paul Ryan refused when asked a direct question in last week’s debate. Specify a deduction, and some pest with a calculator will point out that it doesn’t add up.

Even Fox News isn’t buying it. Ed Gillespie, a senior adviser to the Romney campaign, said on Fox News Sunday that Mr. Romney would work out those details later with Congress. As the program’s moderator, Chris Wallace, pointed out, that’s like offering voters the candy of a 20 percent tax cut without mentioning the spinach they will have to eat.

The Romney campaign claims it has six studies proving it can be done, but, on examination, none of the studies actually make that point, or counterbalance the nonpartisan analyses that use real math. Two of the studies, for example, were done by the same Republican economist, Martin Feldstein, an adviser to the Romney campaign, who said it would require ending all deductions for everyone making $100,000 or more. But Mr. Romney has explicitly said he would not do that.

It is increasingly clear that the Romney tax “plan” is not really a plan at all but is instead simply a rhapsody based on old Republican themes that something can be had for nothing. For middle-class taxpayers without the benefit of expensive accountants, the bill always comes due a few years later.