With the help of Jon Elster and Cristina Bicchieri, I think I have a handle on it. Obama is a conscientious bargainer, but a slow learner. To see this more clearly, let's use something I can't use very well: game theory.
Classic two player games are designed to show what rational actors would do given specific known payoff formulations. For example, consider this:

Barack Obama is not rational, at least not in the simple formulation depicted in this game. He has commendable, but in this political environment naive, faith in bargaining. For Obama, the game looks like this:

Obama has confidence that as political opponents negotiate, the ability to accomplish even greater things - grand bargains - emerges. He's not wrong. A body of theory I often return to - Putnam's work on social capital - informs us that repeated engagement helps build trust and patterns of reciprocity. We get better at working together the more we try. This allows us to risk things that we might not attempt otherwise. We feel less vulnerable, because we have confidence that our opponents/collaborators will not take advantage of a concession. To illustrate what I mean, imagine a school board and a teachers' union making some difficult decisions about how to keep schools open in the face of a budget crisis. The teachers and the administrators have had a history of encounters, bargaining over issues large and small, and across that iterative history of encounters, the two sides have learned that, although they view challenges through different lenses, each side wants to serve the public good, and educate as many kids as possible, as well as possible. With that in mind, the two sides might agree to a bargain that cuts pay for new teachers, preserves pay for more experienced teachers, and creates a process requiring neighborhood school boards to make recommendations about how, and under what criteria, new teachers are given tenure and higher pay. The school board gets the cuts it wants, but surrenders some control over how teachers are assessed and rewarded. The teachers make some concessions regarding entry-level pay, but map out approaches to promotion that allow teachers working in difficult settings - violent, low income neighborhoods filled with struggling families, for example - to be evaluated by context-relevant criteria. It's a socially preferred outcome - schools stay open, teachers stay on the job - that might not be possible if the two sides were negotiating without trust and expectations of reciprocity.
Obama's problem is that he is negotiating with opponents who have no interest in serving the public good. He has been too slow to learn this, perhaps because his faith in the value of iterative negotiations is too strong. He believes in engagement, and the power of long-term rationality. If Republicans and Democrats continue to work together, he believes each party can get some of the things they want and the country will be better off. But he's misjudged his opponents, while they have quickly learned to take advantage of his vulnerabilities. What we get is something like this:

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