Together we will go to a magical realm where two plus two equals eleven. Photo: Justin Sullivan/2012 Getty Images

Let’s stop this meme before it gets started. Mitt Romney did not say that a salary between $200,000 and $250,000 a year counts as “middle income.” I suppose you could say he asserted that if you used the truth standards of the Romney campaign — which allow you to clip phrases to change their meanings or even to present a person quoting something he disagrees with as his own position — but those aren’t truth standards I’d care to live by.

What Romney actually said, in his interview with George Stephanopolous, was that he would not raise taxes on people earning below that level. Here Romney is trying to wriggle out of a trap he blundered into. He has promised to extend the Bush tax cuts and then reform the tax code in such a way as to hold revenue constant, lower tax rates by 20 percent, and close loopholes. This was a vague enough plan that Romney believed he could get by without making any of the ramifications clear, except the good stuff about cutting tax rates. But the Tax Policy Center ran the numbers and found that, even if you granted Romney a series of optimistic to wildly implausible assumptions, he would have to raise taxes on the middle class, by a lot. The rate cuts would lose so much revenue for the rich that there wouldn’t be enough to gain from reducing deductions.

Republicans have been frantically denying the math, which Obama has turned into the potent (and accurate) accusation that Romney’s plan would cut taxes on the rich in order to raise them on the middle class. Republican economist Martin Feldstein tried to defend Romney by doing his own study showing that Romney’s math could work, but in an epic blunder, inadvertently confirmed the charges. Despite cutting all kinds of methodological corners, Feldstein’s study found that the threshold above which Romney would have to raise taxes was not the $250,000 he promised but $100,000 a year. That means Romney would have to raise taxes on a huge chunk of income below $250,000 a year, just as the TPC study found. Feldstein dealt with this problem by writing his column about his study as if it disproved rather than confirmed the TPC, and other conservatives have gone on pretending the same thing.

The Wall Street Journal editorial page today hilariously, if unsurprisingly, cites Feldstein’s study as proof that Romney is right and the TPC study is “discredited.”

In his interview, Stephanopolous brought up Feldstein’s botched rescue attempt. Romney dances around but confirms that his threshold for not raising taxes is $250,000 a year, not $100,000:

GEORGE STEPHANOPOULOS: You cite your own studies. But one of the studies you cite by Martin Feldstein at Harvard shows that to make your math work, it could work, if you eliminate the home mortgage, charity, and state and local tax deductions for everyone earning over $100,000. Is that what you propose? MITT ROMNEY: No, that’s not what I propose. And, of course, part of my plan is to stimulate economic growth. The biggest source of getting the country to a balanced budget is not by raising taxes or by cutting spending. It’s by encouraging the growth of the economy. So my tax plan is to encourage investment in growth in America, more jobs, that means more people paying taxes. So that’s a big component of what allows us to get to a balanced budget. GEORGE STEPHANOPOULOS: But his study, which you’ve cited, says it can only work if you take away those deductions for everyone earning more than $100,000. MITT ROMNEY: Well, it doesn’t necessarily show the same growth that we’re anticipating. And I haven’t seen his precise study. But I can tell you that we can lower our rates — GEORGE STEPHANOPOULOS: Well, you cited the study, though. MITT ROMNEY: Well, I said that there are five different studies that point out that we can get to a balanced budget without raising taxes on middle income people. Let me tell you, George, the fundamentals of my tax policy are these. Number one, reduce tax burdens on middle-income people. So no one can say my plan is going to raise taxes on middle-income people, because principle number one is keep the burden down on middle-income taxpayers. GEORGE STEPHANOPOULOS: Is $100,000 middle income? MITT ROMNEY: No, middle income is $200,000 to $250,000 and less. So number one, don’t reduce — or excuse me, don’t raise taxes on middle-income people, lower them.

What Romney’s doing here is retreating into incoherence. TPC examined his promises — cutting rates by 20 percent, not raising taxes on investment income, and not reducing revenue below Bush tax cut levels — and found they could only add up if you raise effective tax rates on income under $250,000 a year. Feldstein found the same thing, despite his partisan attempt to present his finding as a vindication of Romney.

Now Romney is saying he won’t raise taxes on any families earning less than a quarter million. But that just means his plan is completely mathematically impossible. He’s probably safer being attacked for making a series of promises that cannot be mathematically reconciled than being attacked for a specific ramification like raising taxes on the middle class. (Alternatively, Romney could just say he doesn’t care how much revenue he’d lose.)

The basic problem for Republicans is that their highest policy priority is to cut the effective tax rate paid by the richest 1 percent of Americans, but the vast majority of the voters don’t share that goal. Handling that problem is the single biggest challenge the Republican party faces. Normally, when a party has an extremely unpopular position, it just jettisons it. But Republicans care so much about this goal that they won’t give it up, which makes sense — you compromise on your secondary goals, not on your primary goal. Still, this ultimately places them in the position Romney finds himself and Paul Ryan and George W. Bush have found as well — the only way they can get elected is to obscure the real trade-offs and make up a bunch of fake numbers.