In the long term it is all quite clear. The USG, either deliberately or by recklessness, devalue the dollar so as to lower the real amount of liabilities owed. Hysterical types wager this will happen overnight. The fact is it has been going on for nearly a decade now.
What is more ambiguous is what will happen in the short term. A resolution will take place before August 2, but perhaps not by agreement. In the remote chance the Repulicans hold the line and do not accept some tax and borrow bill, Obama will surely invent some nonexistent executive authority and raise the ceiling anyway. Disturbingly, he will come off as a savior while being a betrayer of the Constitution.
Hopefully it will not come to that. Here are, as if the possibilities were thoroughbreds, my handicapping of the race:
Bipartisan deal raising taxes and cutting spending before August 2- 25%
Bipartisan deal with only spending cuts- 40%
President invents power to unilaterally lift ceiling- 20%
President invents way to keep spending using found money from someplace else in budget-15%
Debt continues to grow- 100%
Sensible libertarian views on nearly everything- except foreign affairs.