The most common reaction is that we will just go through this again in January. Possibly, but there are some reasons to suspect not.
1. The Republican leadership and a significant portion of the funding base for the Republican party understand what a disaster this was. They will work hard to avoid it. While it remains to be seen if Chamber and others will make good on their threat to mount primary challenges to Tea Party incumbents, they will certainly more heavily fund moderates. This will give the moderates more courage to stand up to the Tea Party faction.
2. The Tea Party reps are True Believer fanatics, but not stupid. And they have suffered a major disheartening defeat. In time, they will regain their swagger, but they are thoroughly depressed at the moment. While all of them will have their own irrational reasons to explain their defeat, they are unlikely to be united on tactics in the next few months. Many will rationalize around the idea of the 'long game' with a strategy to avoid risking direct confrontation on this scale.
3. Republicans generally, and to some degree even the Tea Party faction, are feeling pressure to actually 'get stuff done.' The Farm Bill is a major issue for the rural guys.
4. On sequester cuts, the basic poison pill to drive Republicans to the table was steep cuts to the military. This turned out to be less effective than expected on the Tea Party faction who (a) being more Libertarian inclined, are not as concerned with maintaining a military capable of aggressive foreign policy, (b) most do not have military bases or military contractors in their districts. But the next round of sequester cuts due to hit in 2014 is sufficiently steep to force the non-Tea Party Republicans (and even some Tea Party Rs) to want to deal. True, they hope to force Ds to disproportionately fund the military rather than social programs, but see below.
5. Ds won by hanging tough and maintaining party discipline. Reid in particular was good about whipping the 'centrist' Dems against even a token gesture at modifying Obamacare via modification of the device tax (which most Dems want to repeal anyway, but is harder to repeal without some sort of offsetting funding source during regular order). Obama showed he had the spine and the nerve to play chicken and not break. In the end, Harry Reid dictated the terms and the Rs accepted.
More than that, Reid also validated the old guard negotiated approach -- including tossing McConnell a bone in the form of a quasi-earmark for a water project.
6. One of the advantages of "iterative game" is the establishment of reputation. I will also add that in D.C., like Hollywood, your reputation tends to be as good as your last project. Democrats go into negotiation with a stronger hand and an energized team, whereas Republicans go into negotiations with a disheartened and divided team anxious to avoid another politically damaging shutdown. The Tea Party faction will still exert influence, but that influence is likely to be diminished.
While this does not mean that negotiations will go smoothly, or that a true budget deal will be reached, it does mean that a shutdown and debt-ceiling crisis is likely to be avoided. Failure to reach an agreement by January is much more likely to result in a clean CR at some level and an extension of the debt ceiling until after the 2014 election, with each side hoping to enhance its Congressional strength and thus its ability to bargain.
So while I do not think we are likely to get a real resolution, I do think the odds are good we will avoid total shutdown in 2014. This will be hailed as 'progress.'