EARLIER IN the presidential campaign, Mitt Romney included a section called “tax” in his economic plan, “Believe in America,” that posed two sensible questions: “How will we generate sufficient revenue to balance our budget without discouraging economic activity, and will the burden of taxation fall equitably on all Americans?” Mr. Romney argued that the tax code is a “Rube Goldberg contraption of bewildering complexity” and called for a “fundamental redesign” of the system with lower rates and a broader base.

Mr. Romney’s point about the need for an overhaul is certainly true. Major tax reform would be a good opportunity not only to simplify the tangled mess of the code but also to align revenue and spending, which are now catastrophically out of whack.

Mr. Romney has also pledged to lower tax rates by 20 percent in a way that would not add to the budget deficit. But how? One approach would be to eliminate a wheelbarrow full of tax breaks. Another would be to slash more spending. Both are painful, yet neither has been fleshed out in detail by the presumptive Republican presidential nominee. Mr. Romney has offered the feel-good temptation of lower taxes without the harsh medicine to follow.

Last week, a research group in Washington attempted to fill in some of the blanks. The Tax Policy Center, a joint venture of the Brookings Institution and the Urban Institute, took the basic provisions outlined by Mr. Romney and ran them through an economic model. The center kept Mr. Romney’s pledge to be “revenue neutral,” not adding to the budget deficit, and to preserve incentives for investment. It also incorporated other ideas Mr. Romney has suggested. In some cases where the Romney campaign has failed to be specific, the group added its own assumptions, but not unreasonable ones.

The study reached two important conclusions. The first is that Mr. Romney’s plan to lower tax rates would take $360 billion out of federal tax revenue in 2015. Offsetting that — keeping the plan revenue neutral — would require eliminating a whopping 65 percent of today’s $551 billion in available tax breaks. That could mean deep reductions in popular benefits such as the mortgage tax deduction, the tax exclusion for employer-provided health insurance and the deduction for charitable contributions. Politically, it sounds impossible. But those are the numbers.

The Romney campaign responded by saying, vaguely, that tax cuts will lead to more economic growth and thus more revenue. But will they be enough? Not likely.

The other conclusion was that Mr. Romney’s tax cuts would not affect everyone equally. The study showed that the net effect would be a tax cut for high-income households coupled with a tax increase for middle-income households. This is because there are just not enough tax breaks to close for the rich, and the big money is in those for middle-income taxpayers.

The bottom line of this exercise is that Mr. Romney has a hole in his balance sheet. He’s certainly right to want a major overhaul of the tax code, but offering the promise of lower rates while ignoring a huge revenue shortfall is not responsible stewardship. He needs to fill in the blanks in his tax policy, and soon.