In game theory, the type of bargaining that occurs when you're threatening to do/allow something really bad to happen is called brinksmanship. A key point of brinksmanship is to have credibility. Which side has credibility on the debt ceiling negotiations?
Obama has credibility that he's willing to go through a long government shutdown and blame the Republicans. He doesn't have to be elected again and many of us understand that he doesn't really want America to prosper economically anyway.
Boehner, on the other hand, has zero credibility. He has caved at every opportunity is most interested in protecting the GOP House majority.
History says the GOP will cave again. Sad, but true.