The debts would keep growing until the global financial system collapses. This is inevitable. The global economy is addicted to debt. The governments are addicted to debt. If suddenly all governments start increasing taxes, cutting government spending and achieving budget surplus, the nations would become very unhappy and this might lead to social tensions. The global GDP might also shrink.
There's still room for growing even bigger debts. The US dollar would also get devalued because of the tremendous debts. This means that paying off debts with a less valuable currency would be easier, but the problem remains.