President Barack Obama and his Democratic allies have been saying for days that a majority of both Republicans and Democrats in Congress support taking up a simple extension of government spending.

At first glance, it might appear they’re right. So why is the federal government’s shutdown now in its fourth day, with no end in sight?

President Obama, speaking at a DC sandwich shop, says that the House has the opportunity to end the shutdown today, if only Speaker Boehner would allow a vote to take place.

The reality is that a complex array of variables and political considerations has kept the House from voting on the “clean” continuing resolution sent to them several times by the Senate. The politics are not so simple – even if many House Republicans privately favor the clean, six-week extension in government spending, they have refused to break ranks and join with Democrats to reopen the government.

Here’s a look at why …

Do most House Republicans support a ‘clean’ continuing resolution?

Maybe privately, but their actions in public belie those sentiments.

A continuing resolution (or “CR”) is exactly what it sounds like: a resolution to continue government spending at existing levels for a length of time. Congress has routinely used these resolutions to prevent a shutdown in the past, especially when they have failed to reach an overarching budget for the fiscal year. A “clean” CR means that there aren’t any extraneous provisions – a repeal of Obamacare, for instance – attached to it.

Democrats have favored using this clean CR to resolve the shutdown, and Republicans have repeatedly had a chance to bring the Senate-passed spending legislation up for a vote, and each time, they have declined. This was most vividly illustrated on Monday night, when, in the hours leading up to a shutdown, House Republicans repeatedly refused to do this, and instead returned legislation to the Democratic upper chamber that would have sought to undo or delay Obamacare.

There are a few key numbers to know in analyzing the state of play: 217, 200, 17, 20, 190, and 1.

Because there are three vacancies in the House right now, it takes 217 votes to pass legislation with a simple majority. There are currently 200 Democrats in the House, which means that they would need 17 Republicans to break ranks (assuming every Democrat were to show up and vote) to pass a clean CR.

According to various whip counts, about 20 House Republicans have publicly endorsed a clean continuing resolution.

And according to reporting from the Washington Examiner’s Byron York, as many as 190 House Republicans privately support a clean continuing resolution.

One of those Republicans – at least according to a spokesman for Democratic Senate Majority Leader Harry Reid – is Boehner himself.

Those numbers are all soft, though. It’s impossible to say how many lawmakers would stick to their private statements if push came to shove, especially if conservative groups worked actively to oppose such a vote.

So why didn’t the House vote on a clean CR?

Heading into the days and hours before the shutdown, Republicans were betting that Democrats in the Senate and Obama himself would blink. Many Republicans argued that the Obama administration feared a shutdown so much that it would relent and agree to concessions on the president’s signature health care reform law.

Sen. Ted Cruz, R-Texas, pins blame on the government shutdown to President Obama and Majority Leader Harry Reid, telling NBC's Casey Hunt "the Democrats want government by crisis, they want shutdowns. This is Harry Reid's shutdown, because he thinks it benefits Democrats politically."

Boehner also led Republicans down this path because of the GOP’s internal political dynamics. After Sen. Ted Cruz, R-Texas, spent the better part of two months galvanizing conservatives behind a strategy to use the shutdown (and the looming debt ceiling) as leverage to undo Obamacare, Boehner and a number of rank-and-file Republicans fell under intense pressure to follow through with the strategy in order to mollify the conservative grassroots.

What’s the deal with Republicans?

Democrats have argued that Boehner has held up a vote on a clean continuing resolution for fear of losing the speakership. They’re not necessarily wrong.

Boehner has always suffered from an unwieldy relationship with conservatives in the House GOP, who have undercut the speaker and his leadership team in various battles in the past. Furthermore, Boehner’s re-election as speaker earlier this year was almost thrown to an embarrassing second ballot after several Republicans staged protest votes against Boehner.

In short, Boehner’s ability to serve is somewhat at the mercy of a small but vocal faction of House Republicans who would threaten to upend a fragile GOP leadership coalition if they finally judged Boehner guilty of conservative apostasy.

So Boehner’s unwillingness to cut off these conservatives is why we have a shutdown?

Sort of. Obama has certainly argued that Boehner’s considerations are the primary obstacle to reopening the government.

“There are enough Republicans and Democrats in the House of Representatives today that, if the speaker of the House, John Boehner, simply let the bill get on the floor for an up-or-down vote, every congressman could vote their conscience -- the shutdown would end today,” Obama said Thursday in Maryland.

Undoubtedly, Boehner would have risked inflaming conservatives – and thereby risked his grasp on the speakership – had he decided to proceed with a vote on the clean CR despite the opposition of the GOP’s most ardent conservatives.

Is the president right, then?

Not really. Though Boehner has refused to bring up a clean CR for a vote, Republicans in the House continue to have his back.

To boot, GOP lawmakers have technically had a few chances to force a vote on the Senate continuing resolution.

Sen. Chris Coons, D-Del., explains how the government shutdown has forced the Treasury Department to furlough most of the employees responsible for enforcing sanctions on Iran and other nations.

Several times this week, Democrats have tried to attach the clean CR to one of the several mini-spending bills advanced through the House by Republicans. The chair ruled these moves out of order for parliamentary reasons, and Democrats in turn asked for a formal vote to table the ruling of the chair.

In short, such a vote would have set aside the parliamentary maneuver, and allowed a clean CR to move forward. But no GOP lawmaker – even those who are on the record in support of a clean CR – broke ranks and voted with Democrats.

Democrats were expected on Friday afternoon to force another key procedural vote that would allow for House consideration of the clean CR. But Republicans are likely to oppose that, too.

Wait, I don’t get it. Why would so many Republicans vote against something they privately support?

It might be true that the vast majority of Republicans in Congress just want this fiscal mess to end before it does any more damage to the GOP. But those sentiments are only theoretical. And there are a number of strategic considerations that come into play for Republicans at this stage of the game.

If House Republicans were to break with Boehner and join with Democrats to pass a clean CR, it would be a giant rebuke to Boehner, hand a major political victory to Obama, and make the political fallout from the shutdown completely for naught.

Moreover, the only real leverage Republicans have left is the debt ceiling deadline on Oct. 17. If Republicans were to concede defeat on the CR and vote for the clean spending measure at this stage, it would be a vote to deprive themselves of leverage and diminish the chances of winning any concession whatsoever from the administration or Senate Democrats.

So is a clean CR completely dead?

The House isn’t past the point of no return, but it’s pretty close. Democrats would need to increase the intensity and amplitude on the small group of Republicans – who are mostly moderates from swing districts – to make good on their endorsement of a clean CR, and break from Boehner. These Republicans haven’t done so yet, and would have to become much more concerned about losing their seats in 2014 before they move into Democrats’ column.

Boehner could also conceivably decide that he’s regained the upper-hand over conservatives in his conference, whom many moderate or establishment-friendly Republicans blame for forcing Boehner into such an untenable negotiating position in the first place.

Until then, though, the government shutdown will continue.

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