The monetary system is frozen because if someone thinks a potential creditor might end up repaying only pennies on the dollar for its debt, the person isn't going to want to risk having his money pooled with all the other pennies-on-the-dollar debt. If the government were to, as expeditiously as possible, announce that much of the bad debt was simply written off (tough luck to the existing creditors) then new creditors would be able to invest with much more confidence.
From what I understand, the situation is somewhat like personal bankruptcy. Someone who has just declared bankruptcy will hardly be regarded as a good credit risk, but will have a much easier time getting honest credit than someone who is clearly imminently facing bankruptcy.
Pop the bubble and the markets will recover.