FOR SEVERAL weeks, we’ve been asking Republican presidential nominee Mitt Romney to explain how he can cut taxes, as promised, without adding to the nation’s debt, as also promised. Now he’s effectively let the cat out of the bag: He can’t.

Mr. Romney’s tax plan calls for reducing income tax rates by 20 percent. The top bracket would go from 35 percent to 28 percent. He has said that he can do this in a revenue-neutral way by eliminating loopholes. While the rich might pay more, he has said, the middle class would pay less.

There are a couple of pitfalls here. The first is that while closing loopholes sounds good — Make those oil companies pay! — the costliest ones are cherished by most Americans. These are tax provisions that promote home ownership, charitable giving, and employer-provided health care and that allow taxpayers to deduct their state and local income taxes. Limiting or eliminating these popular “loopholes” would be extremely difficult.

The second obstacle, as shown by the Tax Policy Center, a joint venture of the Brookings Institution and the Urban Institute, is that Mr. Romney’s plan is mathematically impossible, even if it were politically feasible. Take away every deduction from every wealthy household, the center calculated, and you still couldn’t make up the revenue the government would lose by reducing rates without raising taxes on middle-class households.

Not so, Mr. Romney protested recently, and cited an analysis by Harvard economist Martin Feldstein, a Romney campaign adviser. Mr. Feldstein said the math could work — if you took away every deduction from every household earning $100,000 or more. (Even then, he couldn’t pay for the estate tax abolition that Mr. Romney also favors, but never mind.) Is that what Mr. Romney has in mind, we asked? If not, what is his plan?

On Friday, ABC’s George Stephanopoulos put the question to the candidate. “No, middle income is $200,000 to $250,000 and less,” Mr. Romney replied.

But then, the Harvard study shows, the math can’t work. His answer? “The biggest source of getting the country to a balanced budget is not by raising taxes or by cutting spending,” he said. “It’s by encouraging the growth of the economy.”

In other words, we are back to counting on magic — to “dynamic scoring,” the voodoo economics of the Reagan era, the wishful thinking of President George W. Bush’s 2001 and 2003 tax cuts that helped turn a surplus into the deficit now weighing the nation’s economy. Cut taxes and hope the economy grows faster than predicted.

At a time when the nation is already on course to build up a debt so large that interest payments alone will begin to drown us, Mr. Romney wants to reduce taxes further, with — it now appears — no plan to make up the difference. It almost takes your breath away.