So here’s where we are: It might be mathematically possible to make Romney’s plan work by sharply increasing taxes on people making between $100,000 and $200,000 so you could cut them on very rich taxpayers. It’s not possible to make the numbers add up if you refuse to raise taxes on people making less than $200,000.

It’s also worth remembering that “mathematically possible” is not nearly the same thing as “politically realistic” or “good idea.” Feldstein, for instance, assumes the elimination of the charitable deduction for these taxpayers. That’s something the Republican National Platform expressly promises Republicans will never do. He assumes the elimination of the standard deduction for these taxpayers, which is, again, very difficult to imagine. Even something as simple as wiping out the home mortgage-interest deduction for wealthier taxpayers seems unlikely for an administration hoping to see a housing recovery.

In my view, TPC’s assumptions are closer to those of others in the political system, and so I’m sticking with “mathematically impossible” as the correct descriptor for Romney’s promise. That said, there would be an easy way for Romney to end this debate: He could come out with a plan saying exactly what he’ll do, or even just a set of principles — like no tax increases on anyone making less than $100,000 — that gives us a hint of how he makes the numbers work.

Tax plans aren’t just about math

It’s worth emphasizing just how low a bar the Romney plan is being asked to clear. The question the Tax Policy Center asked was whether it’s mathematically possible to do all the things Romney says he wants to do. But even if it were mathematically possible, it may not be politically possible or substantively wise.

All of the above analyses assume that Romney totally eliminates the charitable deduction, mortgage-interest deduction, all education tax breaks, all state and local tax deductions the employer-provided health care exemption, all Health Savings Account and medical expenses deductions, and more for people making over $200,000. Even if TPC is wrong, you’d probably have to limit them for people making under that amount too, so middle-class people pay the same amount when you take into account the rate cuts.

These are enormous changes. Eliminating the charitable deduction for the rich could effectively wipe out funding for thousands of charitable, artistic, and educational institutions. Small theaters could shut down. Anti-malaria groups would buy fewer bednets. Private colleges would lose donations, and hike up tuition to make up the difference, even as tuition deductions and credits are eliminated. In 2009, when President Obama proposed simply limiting the charitable deduction at the to end, Martin Feldstein, author of the first study trying to show Romney’s plan could work, wrote, “in effect, the change would be a tax on the charities, reducing their receipts by a dollar for every dollar of extra revenue the government collects. It is hard to imagine a rationale for taxing schools, hospitals, medical research budgets and arts organizations in this way.”

Eliminating the mortgage-interest deduction would upend the housing sector, reducing demand to buy dramatically and shifting the sector toward renting. Eliminating the employer health exemption could mark the beginning of the end of the employer-based health system as we know it.

Perhaps these are good ideas. Many countries’ tax codes are less tolerant of charitable contributions than the US and make up for that with direct artistic and educational subsidies. The mortgage-interest deduction arguably fueled the housing bubble. The employer-based health care system keeps people from moving freely between jobs, and ending the exemption that keeps it in place could do a lot of good. But these aren’t just technical changes. They’re transformative shifts in American public policy. And the debate over whether they would make Romney’s plan possible has obscured the debate over whether they’re a good idea, or likely to happen.

But as even Diamond says, this is all nothing more than an academic exercise.

The rub is in all those details that Romney refuses to release about which tax breaks he would scrap. There’s a reason he doesn’t want to talk about them: The choices are ugly. You have only a few big targets to finance a big income-tax cut. They include credits and deductions that are extremely popular with swing voters, such as the child tax credit and deductions for mortgage interest, health care benefits, and charitable contributions.

The only way a big tax-overhaul will pass, Diamond said, is if a president takes hold of a bunch of those popular credits and tries to sell voters on why they should give them up.

“This type of reform will never happen if there’s not presidential leadership and the president’s not fully committed, and there’s not some bipartisan agreements,” he said, adding: “I just don’t see any way that’s going to happen right now. I don’t see [Senate Majority Leader] Harry Reid or [House Speaker] John Boehner agreeing on anything – I don’t care if it’s now, or after the election, or six months from now, or 10 years from now.”

The odds of such a tax plan passing would increase, Diamond said, if a presidential candidate would lay out and own the tough details on the campaign trail. He doesn’t expect that to happen. Nor would he advise it, politically.

“To be honest,” Diamond said, “I don’t understand why Romney’s put out as much information as he has. I would have put out a lot less.”