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How long the shutdown will last — probably the first question on many Americans' minds this morning — depends on Congress reaching agreement on a government-funding bill. In other words, the same roadblock that began the shutdown in the first place. But now that the shutdown is underway, a happy resolution for Republicans only becomes less likely.

A reminder of how we got here. The House, acting at the behest of its conservative Republican core, sent the Senate three slightly varied versions of the same proposal: give up part of the Affordable Care Act (Obamacare) in exchange for funding the government. The Senate rejected the idea each time.

On Monday night, the House suggested a conference between the two chambers, apparently hoping for a compromise. Senate Majority Leader Harry Reid's response encapsulates the moment: He rejected the idea, saying that Senate Democrats "will not go to conference with a gun to our head." Pass a short-term funding bill and reopen government, he suggested, and the Senate would talk about a longer-term agreement. Sure enough, the Senate on Tuesday morning voted on party lines against going to conference.

In conversation with The Washington Post, "senior Republicans" figured the shutdown would last "at least a week." There are time-consuming aspects to the House's proposed resolution — even in conference, a deal would need to be worked out and then votes would need to be taken — but an estimate of a week seems lengthy even in that context. Which suggests that House Republicans are pessimistic about being able to budge their Democratic opposition.

As Monday unfolded, the Republicans' position apparently weakened. Members of the party in the Senate lambasted their House colleagues. There was a tepid and unsuccessful "revolt" by Republican moderates pushing for a funding bill that didn't include the anti-Obamacare amendments. Over a dozen House Republicans, mostly conservatives, voted against the party's last offering. Senate Democrats, on the other hand, never displayed any dissension.

Despite the best rhetorical efforts of Republican party leaders, it's obvious that their insistence on trying to undermine Obamacare using the pressure point of the federal budget caused the current crisis. Bear in mind: this is following repeated attempts — over 40 votes in the House — to revisit Obamacare through the legislative process. And, as many were quick to note, it was after 18 attempts by Senate Democrats to go to a conference committee to negotiate on a new budget.

Once the shutdown went into effect Monday night, the politics shifted even more strongly against the Republicans. A poll from Quinnipiac University released on Tuesday morning suggests that Americans are generally unhappy with the work of Congress, but hold Republicans largely responsible for the current situation. Only 32 percent of Americans approve of the work of congressional Democrats — but that's twice as many as approve of the Republicans. Americans prefer Obama's handling of health care over Congressional Republicans by a 47 to 38 margin. But most significantly, Americans are nearly three-to-one against shutting down the government to block the implementation of Obamacare, including a spread of only about 5 points among Republicans themselves.

When Sen. Ted Cruz of Texas launched his 21-hour speech last week, he repeatedly referred to the will of the American people, noting how the outcry against Syria apparently led President Obama to rethink his position. On this cause, which Cruz has championed for months, the loudest voices have been from the far-right, advocating for a shutdown instead of moving forward with Obamacare. (Though, of course, Obamacare's insurance exchanges launched on Tuesday despite the shutdown, right on schedule.)

As the shutdown continues, it seems likely that a lot more people will speak out a lot more loudly in favor of resolution of the shutdown. The "moderate revolt" on Monday night, reportedly reflecting the will of a silent majority of House Republicans resulted in only two votes against the anti-Obamacare amendments. It's hard to see how public pressure from vocal constituents seeking resolution of the shutdown will do anything but increase the boldness of whatever moderate Republican contingent exists. And Democrats are doing what they can to foment that sort of outcry, running automatic calls in moderate Republican districts.

The paths to resolution, then, look like this.

Option 1 is that House Republicans, a group notoriously unwilling to offer any appearance of compromise, pass a continuing budget resolution funding the government but without the poison pill of an anti-Obamacare amendment. The Senate approves that resolution, which would probably only last a few weeks, and the president signs it. Government re-opens. The two chambers go to conference; a longer-term budget deal is reached.

Option 2 is that the Senate gives in first, agreeing to go to conference with the Republicans —perhaps at the behest of a president eager to get the government back at work, or, depending on how this lasts, in an effort to get the budget resolved before Congress needs to tackle the even-more dangerous debt ceiling debate. In conference, the Senate and House agree to some compromise that doesn't significantly affect Obamacare (though it may rescind a tax on medical devices that House Majority leader Eric Cantor strongly opposes). (Update, 10:15 a.m.: Sen. Dick Durbin suggested a possible compromise on that tax.) Both chambers pass the measure, the president signs it, and government re-opens.

Option 3 is that the two sides go to conference and the House extracts some significant concession on Obamacare. It is actually not clear how this could happen, barring some massive spike in public sentiment in favor of resolving the shutdown at the expense of the already-underway Obamacare rollout. (The trend in polling has been the opposite; opposition to using the government as leverage in this way is increasing.) The president, for some reason, signs it and government re-opens.

For House Republicans, any resolution needs to include a key feature: it needs to help them save face. That makes the second option one of the more likely ones; at this point, even going to conference is something of a win for the Republicans. (Setting aside the fact that an agreement to fund the government at current, sequestered levels is itself a win for conservatives.) And, tacky as it sounds, winning is what politics is all about. As noted by BuzzFeed, the current crisis is the continuation of a years-long effort by Republicans to beat Obama, which failed most spectacularly last year. The problem for the party is that their Senate and administration opponents like to win, too, and are not likely to extend a sturdy branch into the quicksand on the president's signature legislation.

This article is from the archive of our partner The Wire.