The full faith of the government, which provides a useful service to the society: a commodity specifically designed to facilitate trade. Fiat money is in theory superior to precious metals and societies should switch to fiat currency naturally, not due to coercion.
As all things related to government, it can go wrong in two main ways:
- democracy fails because access to power is severely limited, say by a closed plutocracy that derives wealth from monetary control
- democracy works but the average voters don't understand economics

In most societies these days a combination of the two problems make fiat money fail to meet it's theoretical potential.