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John Boehner announced on Tuesday that he will proceed with a plan to suspend the federal debt ceiling, which is actually kind of a brilliant way to avoid crashing the world economy without voting for something that sounds like it increases the national debt. But, as part of his concessions to the looniest wing of the Republican party, he has also committed himself to passing a budget that would reach full balance within a decade.

Paul Ryan’s budget, even while employing all sorts of fanciful projections, didn’t balance the budget until 2040.Why? Because the parameters Republicans have picked for the budget make balancing the budget utterly impossible. Moving that timetable up by seventeen years changes the plausibility level from Level: Unicorn to Level: Unicorn Being Ridden By Santa Claus Who Has Lost 50 Pounds Through One Weird Trick. (That’s why Santa’s riding a unicorn now — otherwise, he’d be far too corpulent.)

Some actual budget wonks are surely working to show this as we speak, but in the meantime, some rough, rough math. According to Richard Kogan of the Center on Budget and Policy Priorities, balancing the budget in 2023 will require an estimated $800 billion in savings that year.

To begin with, the GOP has ruled out any tax increases. (Indeed, the $800 billion includes the tax hikes on the rich from January 1 that most Republicans voted against — knock those tax hikes out, and you’d have to cut more.) House Republicans also don’t want to cut defense — indeed, they have voted consistently to increase defense spending over current levels. But to be charitable, we can assume the defense spending increase proposals fail.

What’s next? There’s Social Security and Medicare. But wait — Republicans have insisted that, as a basic principle of fairness, we cannot touch those programs for anybody 55 years or older. (They “should not be forced to reorganize their lives,” says Paul Ryan.)

So what’s left? You have, mainly, programs for the poor and very sick, like Medicaid, child nutrition, unemployment benefits, and so on. Then you have domestic discretionary spending, which is basically all the major functions of government that aren’t either defense or writing a check to people — infrastructure, food inspectors, scientific research, and on and on. Republicans have already forced Obama to accept extremely tight caps that would cut domestic discretionary spending to well below its lowest level as a share of the economy in decades. How those caps would actually be implemented when it comes time to impose the cuts, I can’t imagine.

But that’s the pot of available savings. It’s around a trillion and a half dollars in 2023. So, that means House Republicans will have to cut domestic discretionary programs and spending for the poor by about half.

Now, if you assume that Republicans aren’t going to actually figure out how to go further than the domestic discretionary cuts they’ve already voted for — I doubt they can actually carry those out — then the available pool of spending is the $900 billion-some dollars spent on programs for the poor and sick: Medicaid, food stamps, etc. So we’re looking at close to a 90 percent spending cut on programs for the poor and sick. I suppose Paul Ryan could spin this as a super-compassionate plan to help starving children and people with awful diseases learn to stop being moochers and take care of themselves.

More likely, you’re going to see more sleight of hand: assuming faster economic growth, magic asterisks galore, and so on. Now, my figures are very back-of-the-envelope. But the inescapable fact is that Boehner has committed now to voting on something that would require even more draconian cuts to social spending than the Ryan budget. It could work! Also, the suddenly slim, unicorn-mounted St. Nicholas might swoop in, impale Obama, and somehow win the budget fight.

Update: Kogan does the full numbers and has a more complete breakdown here.