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.