President Obama sat down with Univision reporter Claudia Botero and told her that he would begin pushing anew for a comprehensive immigration reform bill as soon as the government shutdown/debt ceiling crisis is resolved. Now, it’s still a bit premature to begin talking about the likely fallout from the shutdown crisis, but one of the arguments I have been making throughout is that the Republicans need to be cleaved in two if we are going to be able to do things like pass a transportation bill, end the sequester, or pass immigration reform.

I can’t say that I am confident that we’ve made a sufficient breakthrough, but we’ve done the preliminary work. Here’s the deal. So long as Speaker Boehner was adhering to the Hastert Rule that says that he can’t bring a bill to the floor that doesn’t have the support of the majority of the Republican Caucus, then most of the president’s agenda was dead on arrival in the House.

That was a very bleak prospect for the president’s second term. There have been a few discrete times when Boehner has been willing to break the Hastert Rule…to avoid the fiscal cliff, for example, and to reauthorize the Violence Against Women Act. But Boehner had to be very selective with these transgressions, lest he invite an internal revolt. Obviously, he was unwilling to stick his neck out to avoid a government shutdown or keep us from coming up against a debt default.

Yet, the Hastert Rule is an artificial rule. It isn’t part of the Constitution or the official rules of the House. There are several parts of the president’s agenda that actually have the support of the majority of the House, if not the majority of Republicans in the House. There is probably majority support for turning off the sequester and transportation and farm bills. There is almost definitely majority support for comprehensive immigration reform.

To get movement on these issues, the prerequisite is that Republican moderates in the House get comfortable with defying the Tea Party movement and working with the president. That is no easy task, considering the way the Republican base feels about Obama. A second prerequisite is that the Speaker, whether Boehner or some replacement, be willing to bring bills to the floor. That is also a heavy lift.

But, if it is going to happen, the only way it could happen is if there is a major rift in the Republican Party between the sane Republicans and the crazy ones. There is no guarantee that this will be sufficient, but it can’t happen without the rift.

Most of the focus on the administration’s strategy has been on their desire to get rid of the leverage the Republicans have used through hostage-taking. What makes this element so important is that the Congress has to pass a budget eventually, and without the hostages, they have to do it sooner rather than later. And they’ll have to actually make concessions rather than just pocketing the administration’s concessions and governing through sequestration. This will quickly put a final inglorious end to the Norquist Pledge, which is a major achievement.

But the cleavage in the Republican Party is arguably more important because, without it, there is no hope of building a governing majority in the House.

I don’t think this governing majority will emerge smoothly, if at all, from the current crisis, but I expect it to kind of evolve over the next few months as the GOP really begins to digest how badly they are divided. Immigration reform could be the vehicle. A battle over the Speakership could be the vehicle. A battle over the Farm Bill could be the vehicle. The next budget or debt ceiling deadline could be the vehicle. In every one of these debates, the fissures in the GOP will be coming to the fore.

So, this battle is going to have real consequences. The political world as we knew it is gone. Something new and different is going to emerge from this crisis, and I hope that it will be a more functional, if not more pleasant, environment.