FORMER GOVERNOR Mitt Romney, the presumed Republican nominee for president, promises to lower everyone’s income tax rate without reducing revenue. This sounds terrific. Why didn’t we think of it sooner?

Mr. Romney says that he can achieve this seemingly magical result by “broadening the base” for income tax collection. This, too, sounds great. In principle, everyone favors “broadening the base,” also known as closing loopholes. But everyone favors closing someone else’s loopholes: those of oil companies, say, or of plutocrats who park their money in the Cayman Islands.

Unfortunately, such inviting targets, to the extent they exist, don’t cost the government much in the overall scheme of things. The “loopholes” that cost most are deductions and other tax provisions that most Americans consider sensible, if not God-given, rights: tax breaks for employer-provided health insurance, which according to the Congressional Budget Office will cost $2 trillion over the next 10 years; for pension and retirement savings ($1.8 trillion); for mortgage interest ($1.6 trillion) and charitable giving ($600 billion). Mr. Romney hasn’t said which of these he would trim or by how much.

Recently the nonpartisan Tax Policy Center, a joint venture of the Urban Institute and the Brookings Institution, showed that Mr. Romney’s plan would by necessity help the rich and hurt the middle class. In an interview with Fortune magazine last week, Mr. Romney took strong issue with this conclusion. “They made garbage assumptions and they reached a garbage conclusion,” he said. Contrary to the center’s assumption, he said, he would not take away middle-class tax breaks for “homeownership, charitable giving and health care.”

Trimming those breaks for the wealthy, as Mr. Romney implies he would do, is a good idea. President Obama has been proposing to do so, by capping total deductions allowed in top brackets, through most of his term, and the idea has gone nowhere in Congress. But here’s the catch demonstrated by the center (and confirmed in an update last week, responding to criticisms from some conservative economists): Even if you take away every dollar of tax breaks the wealthy enjoy, you won’t get as much back as Mr. Romney proposes to give in tax cuts. So you would either have to go after the middle class or abandon the promise of revenue neutrality.

If these are “garbage assumptions,” why doesn’t Mr. Romney let us in on his own? If he can be specific about how much he would lower the tax rate, why not be as specific about how he would pay for that? A spokeswoman responded: “Governor Romney has announced clear and specific principles for his tax reform plan and will work with Congress to write a bill that achieves them.”

In reality, his principles are mutually exclusive: You can’t simultaneously lower tax rates, take in as much money as before and protect the middle class. There may be no politically feasible way, and there’s certainly no politically popular way, to “broaden the base” enough to pay for Mr. Romney’s tax cuts. It’s reasonable to assume that his cuts would, as did President Bush’s, worsen the nation’s deficit.

Until he’s willing to explain how he would avoid such a result, he has little standing to criticize Mr. Obama’s fiscal shortcomings.