So you have this neighbor who has been making your life hell. First he tied you up with a spurious lawsuit; you’re both suffering from huge legal bills. Then he threatened bodily harm to your family. Now, however, he says he’s willing to compromise: He’ll call off the lawsuit, which is to his advantage as well as yours. But in return you must give him your car. Oh, and he’ll stop threatening your family — but only for a week, after which the threats will resume.

Not much of an offer, is it? But here’s the kicker: Your neighbor’s relatives, who have been egging him on, are furious that he didn’t also demand that you kill your dog.

And now you understand the current state of budget negotiations.

Stocks surged last Friday in the belief that House Republicans were getting ready to back down on their ransom demands over the government shutdown and the debt ceiling. But what Republicans were actually offering, it seems, was the “compromise” Paul Ryan, the chairman of the House Budget Committee, laid out in a Wall Street Journal op-ed article: rolling back some of the “sequester” budget cuts — which both parties dislike; cuts in Medicare, but with no quid pro quo in the form of higher revenue; and only a temporary fix on the debt ceiling, so that we would soon find ourselves in crisis again.

I do not think that word “compromise” means what Mr. Ryan thinks it means. Above all, he failed to offer the one thing the White House won’t, can’t bend on: an end to extortion over the debt ceiling. Yet even this ludicrously unbalanced offer was too much for conservative activists, who lambasted Mr. Ryan for basically leaving health reform intact.

Does this mean that we’re going to hit the debt ceiling? Quite possibly; nobody really knows, but careful observers are giving no better than even odds that any kind of deal will be reached before the money runs out. Beyond that, however, our current state of dysfunction looks like a chronic condition, not a one-time event. Even if the debt ceiling is raised enough to avoid immediate default, even if the government shutdown is somehow brought to an end, it will only be a temporary reprieve. Conservative activists are simply not willing to give up on the idea of ruling through extortion, and the Obama administration has decided, wisely, that it will not give in to extortion.

So how does this end? How does America become governable again?One answer might be that we somehow stumble through the next 13 months, and voters punish Republican tactics by returning the House to Democratic control. Recent polls do show a large Democratic advantage on the generic House ballot. But remember, Democratic House candidates already “won” in 2012, in the sense that they received more votes in total than Republicans. Yet the vagaries of district boundaries — partly, but not entirely, the result of gerrymandering — meant that the Republican majority in seats remained, and it would probably take a really huge Democratic sweep to dislodge G.O.P. control.

There is, however, another solution, and everyone knows what it is. Call it Dixiecrats in reverse.

Here’s the precedent: For a long time, starting as early as 1938, Democrats generally controlled Congress on paper, but actual control often rested with an alliance between Republicans and conservative Southerners who were Democrats in name only. You may not like what this alliance did — among other things, it killed universal health insurance, which we might otherwise have had 65 years ago. But at least America had a functioning government, untroubled by the kind of craziness that now afflicts us.

And right now we have all the necessary ingredients for a comparable alliance, with roles reversed. Despite denials from Republican leaders, everyone I talk to believes that it would be easy to pass both a continuing resolution, reopening the government, and an increase in the debt ceiling, averting default, if only such measures were brought to the House floor. How? The answer is, they would get support from just about all Democrats plus some Republicans, mainly relatively moderate non-Southerners. As I said, Dixiecrats in reverse.

The problem is that John Boehner, the speaker of the House, won’t allow such votes, because he’s afraid of the backlash from his party’s radicals. Which points to a broader conclusion: The biggest problem we as a nation face right now is not the extremism of Republican radicals, which is a given, but the cowardice of Republican non-extremists (it would be stretching to call them moderates).

The question for the next few days is whether plunging markets and urgent appeals from big business will stiffen the non-extremists’ spines. For as far as I can tell, the reverse-Dixiecrat solution is the only way out of this mess.