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Samuel Beckett’s famous phrase “You must go on, I can’t go on, I’ll go on” is a pretty good summation of what will face Treasury come August 3 if there’s no deal on the debt limit. Reuters has a fantastic story this evening on the impossible quandary facing Treasury officials should the unthinkable come to pass; purely as a practical matter, it’s far from clear that it’s even possible to stop making the 3 million payments that Treasury makes automatically every day. Doing so involves a massive computer-reprogramming effort which I’m sure could not be implemented overnight — and for political reasons nobody is going to get started on such an effort until after all hope is lost for a deal in Congress.

Realistically, then, the government is likely to breach the current debt ceiling no matter what Congress agrees. A failure to lift it would be a bit like an edict to a steaming supertanker that it had to stop dead: no matter how much force of law that edict has, sheer momentum is going force many basic operations of the public fisc to continue for some period of days or weeks.

At that point — and no earlier — there would be enormous pressure on the White House to pull out the 14th Amendment and declare the debt ceiling unconstitutional, if only for practical reasons: doing so would be a lot easier than trying to reprogram the computers which are set to send out $49 billion of Social Security checks on August 3. Not to mention that no president ever wants to be the person who stiffed America’s seniors on their guaranteed monthly income: a greater failure of leadership can hardly be imagined. On the other hand, saying “enough of you bickering legislators, I’m sworn to uphold the Constitution and do what’s in the best interest of the country” is much more presidential.

That said, it’s easy to see why the official Treasury position is about as hardline as it gets:

“Our plan is for Congress to pass the debt limit,” Geithner said late in May. “Our fall-back plan is for Congress to pass the debt limit, and our fall-back plan to the fall-back plan is for Congress to pass the debt limit.”

The August 2 deadline is real, and no responsible legislator would risk letting it pass. Beyond that date is uncharted territory: Here Be Dragons stuff. Real uncertainty, as opposed to risk: anything could happen, including some extremely catastrophic outcomes related to payment default on maturing Treasury securities.

For the time being, the markets are buying it. The latest Treasury auction of four-week bills came in at 0.000% — Treasury is getting the money, literally, for free. And the maturity? August 4 — two days after the August 2 deadline. It’s entirely possible that Treasury simply won’t have the money to repay this principal. And yet that possibility clearly isn’t priced in — partly because it can’t be priced in, and partly because of auction dynamics: the bidders who won the auction are precisely the people who aren’t worried about the debt ceiling.

According to the Reuters report, a “small team of Treasury officials” is trying to work out what might happen come August 3 — can payments be delayed? Can the Constitution be invoked? Can the government prioritize payments? (It seems to me that if the debt ceiling is real, it would have to, it wouldn’t have any choice.)

The really depressing thing is that even if a deal does get done this month, the planning won’t have been in vain. Now that the Republicans can see how much leverage the debt ceiling gives them, they’re going to pull this stunt every time it gets near. The best-case scenario, with a big $2 trillion increase, would mean that we’re going to go through the exact same thing late in 2012; a more modest increase in the debt limit would set up a reprise of the current fiasco much sooner.

And that’s the invidious thing about low-probability events. Repeat the experiment often enough, and eventually they’ll happen. We’ll get a deal done this time. But one day, we won’t. And that day is not going to be a happy one.