Setting aside the hourly thrust and parry between Democrats and Republicans, here’s how the shutdown is likely to end: Senate Majority Harry Reid is going to strike a deal with his Republican counterpart Mitch McConnell at some point in the next few days. The deal will reopen the government for a medium length of time—possibly till January 15, when the next round of sequester cuts kick in—giving the two sides time to replace the sequester with something more appealing. The deal will also raise the debt ceiling—maybe for as little as a few months, maybe until after the 2014 election. Reid will give up almost no concessions in return for any of this, with the exception of one or two symbolic items, and he’ll probably get some higher-than-sequester level of government funding (a top Democratic priority) for a month or two starting later this year. Pretty much every Democrat in the Senate will vote for the deal, along with at least five and maybe as many as 20 Republicans.

As the minutes tick away toward default this Thursday, the Reid-McConnell arrangement will be the only deal in town. With no alternative to avoiding a default, House Speaker John Boehner will add some small face-saving alteration and bring it to the floor, where it will pass with several dozen Republican votes and a large majority of Democrats. In doing so, Boehner will reprise the same formula he deployed in resolving last year’s fiscal cliff fight. I know this because it’s how the GOP has gotten out of pretty much every self-inflicted PR disaster of the Obama era, and it’s where the best reporting available suggests we’re headed today.

Of course, I could be wrong on the details. If Reid plays his hand especially well, he may do a bit better—erasing more of the sequester now rather than deferring that task till later. If McConnell plays his hand especially well, he may get some slightly bigger concessions, like a delay or repeal of the tax on medical devices that was enacted under Obamacare. But those are the basic contours of what a deal will look like, and they’re notable for what they almost certainly won’t include: anything that has more than a trivial effect on Obamacare, any cuts to entitlements as the price of reopening the government or raising the debt ceiling (though Democrats may give a bit on entitlements in exchange for ending the sequester and some new revenue). Which is to say, the deal will include none the key demands the Republicans were hoping to achieve by shutting down the government.

Or, put differently: On policy, the Republicans will end up either about where they were when they started this fight, or worse off. Politically, they’ll be in a far weaker place, having seen their public support collapse. Along both dimensions, they are faring worse than they did even in 1995-6, when Bill Clinton accepted some of their key demands, and when their approval ratings didn’t sink as low as the latest polls suggest they’re sinking now.

How has it come to this? After all, there were reasons to think Republicans would be in a stronger position today than in the mid-‘90s. As my colleague Nate Cohn and other stats connoisseurs have pointed out, the public is more polarized along ideological lines than it was back then. That means a party can do its level best to piss off the entire country—and the GOP has really thrown itself into the challenge—and still retain the support of 45 percent of voters.