To elucidate the mysteries of Washington — in particular, why House Republicans, having compelled the Democrats to craft a Republican-in-all-but-name plan to get a deal on raising the debt ceiling, still don’t want a deal — we turn to the Fable of the Scorpion and the Frog.

A scorpion meets a frog on the bank of a stream and asks the frog to carry him across on his back. The frog asks, “How do I know you won’t sting me?” The scorpion answers, “Because if I do, I’ll drown along with you.” So the frog, bowing to the logic of the scorpion’s answer, sets out across the stream with the scorpion on his back. About midstream, the scorpion stings the frog, who is paralyzed and starts to sink — as does the scorpion. “Why?” the dying frog asks. “Because it’s my nature,” the scorpion replies.

Refusing to reach a deal on raising the debt ceiling has cost Republicans in the court of public opinion. Virtually every poll shows that the public would blame them more than they would President Obama or congressional Democrats if the government does, in fact, default. While a default would doubtless wound Obama, as it very likely would hurt the U.S. and global economies, any rational calculation of self-interest would surely compel the GOP to come to terms. That’s why the financial markets, which base their calculations on the assumption that people — certainly, major groups — act in their own self-interest, have believed that a deal would eventually be struck.

But the frog assumed the scorpion would act in his own self-interest, too.

Now, in some standoffs, acting with apparent indifference toward the disastrous consequences that loom — behaving, that is, as though one is bereft of rational calculation — can be the rational thing to do. It may make your opponent concede more than he would otherwise. The GOP’s intransigence in the face of one concession after another from the president — abandoning, successively, his party’s insistence that tax increases should be a substantial part of any fiscal fix, then that Social Security and Medicare should not be touched, and finally that tax increases should be part of the deal at all — has certainly given them more substantive victories than virtually anyone anticipated. But of course, few anticipated how incapable Obama would be of framing the larger debate, and how willing he’s been to jettison core Democratic positions in his bid to win back the support of independent voters.

The most recent Democratic proposal in play, from Senate Majority Leader Harry Reid, meets the Republican right’s long-standing demands for a deal that reduces federal spending by the amount that the debt ceiling would be raised, and that contains no tax increases whatsoever. It has won the backing of Nancy Pelosi, the House Democratic leader and the de facto leader of congressional liberals, who began her statement of support with the words, “It is clear we must enter an era of austerity.”

Even if Republicans have painted themselves into a political corner, they have also painted the Democrats into a substantive corner — though they couldn’t have done it without Obama’s assistance. By striking a deal with Reid, they may escape their political corner, leaving Democrats stuck with a deal that undermines their party’s ideological foundations.

But is that even what the Tea Party Republicans (and, these days, all Republican elected officials are either in the Tea Party or afraid of it) really want? Many of the Tea Party House freshmen clearly see their role as voting for their Ayn Rand fantasies and then going home. With the House having passed the “cut, cap and balance” bill (which would decimate entitlements) on a near-party-line vote last week, “what else is there?” New York Republican Michael Grimm wondered, as The Post reported Monday. “At this point, honestly, I don’t think there’s any more the House can do.” Pennsylvania freshman Mike Kelly echoed Grimm’s sentiments: “The House has done everything it could do,” he said. “Now, what’s the holdup?”

Apparently, House Republicans are holding out for a formal surrender ceremony. Speaker John Boehner has come up with a counterproposal to Reid’s — a plan that isn’t all that different substantively but that Boehner titled “The Two-Step Approach to Hold President Obama Accountable.” For many Republicans, even this doesn’t go far enough. Republicans apparently won’t be satisfied until Obama takes responsibility for all of the national debt, the Bush tax cuts and the Oklahoma heat wave, admits he’s not a citizen and goes back to Kenya.

They may harm themselves and the nation by holding out for that deal. Like the scorpion, though, it’s their nature.