Republicans are very good about getting into wars of choice. They just have no clue about how to get out. Iraq was one example. The debt-ceiling/government shutdown wars are another. [Just a little footnote: chaos historically is the recipe for right-wing takeovers].
Although there will be a lot of caterwauling about providing the right-wing a lifeline for their reckless behavior, prudence demands it, so long as they do not get a concession. One does not allow misbehaving or even destructive toddlers to keep the entire family from going to the beach.
Not only do I heartily endorse the president's "no negotiation" stance, I believe I was the first to suggest it, preceding the first debt-ceiling fiasco by six months, before it was even a gleam in the Koch Boys' eyes. But, chaos and disaster would be almost as great a victory for them as capitulation.
So, the only way out -- and here one depends not on Koch-inspired crazies, but on the suburban Republicans who have found themselves hijacked and could, if they were of a mind, become the true power base in the Congress -- is to find something that a) requires no negotiation since everyone agrees, thereby keeping the president's pledge; and b) provides the moderate Republican lawmakers enough to justify their support in their caucus.
The one policy that, so far as I know, fits those criteria is corporate tax reform. The president mentioned it in his second inaugural, Republicans have claimed it will lift the economy -- although, curiously, never did anything about it while they held power -- much work has been done on it, and virtually all actors have provided similar outlines: revenue neutral, lowering rates, broadening the base, closing loopholes. [Footnote: determining "revenue neutral" will be an interesting exercise, if they take what they actually pay versus what they are supposed to pay].
Now, such an act of prestidigitation cannot happen in days, perhaps even months. So, the 'deal' here could be to end the shutdown, pass a debt-ceiling increase to 2015, and appoint a commission to recommend a corporate tax reform bill that must report before the end of 2014 with a pre-agreement that that proposal gets an up-or-down vote prior to the expiration of this Congress.
The problem, of course, is that the Democrats cannot offer to do this. Once they do, Republicans will just take it as another concession, and demand more.
Republicans can, however, pass it in the House, and have a field day rallying behind it, talking about what wonderful things it will do for the economy (it won't, but that is another story), and even exhorting the president to join them as he himself suggested it.
In this scenario the president has not agreed to anything he opposed, and Republicans have 'won' something they wanted. There is no guarantee that the commission's proposals would be passed, that will depend on the predisposition of this Congress, and the president, after the 2014 elections.
Then, it will be on to the next government shutdown in 6 weeks after the CR-extension expires. By that time, however, the Republican moderates will have shown that they, not the Democrats and not the Tea Party, control the balance of power in Congress.
Perhaps the old saw, "nothing succeeds like success," will spur them to act for the sake of sanity again. One can only hope.