It seems Obama really understands that if he does not handle this situation he truly risks becoming the worst president ever. This is not hyperbole, this is really what is at stake at the moment.
Probably the stupidest decision Obama every made was try to use the debt ceiling to force all sides to adopt his grand bargain. He both failed and did serious damage to the economy. Far more importantly, he undermined the entire office of the President.
Establishing the precedent that Congress could force the President to do anything they want by threatening to default would strip the office of its veto power. If the President ever vetoed anything, Congress would just need to wait to attach it to the next debt ceiling vote to get it. The executive branch would become a shadow of its former self. Obama needs to stop it now or risk it becoming a serious long-term problem.
These are the kinda of fights that have defined nations. In the past similar showdowns between parliaments and kings ended up turning real monarchs into mostly powerless figureheads.
If Obama’s real legacy was being the President who let the White House be defanged by Congress, history might very well remember him as the worst president ever. It appears Obama understands the stakes.