Money is fiction. The value of money is derived from trust in the central authority that creates it. Therefore I think an entity like Bitcoin (though not necessarily Bitcoin itself) could conceivably come to replace federal currency because its source is not human beings, but an unflappable algorithm.
The source of the currency is software written by humans and run on computers built and controlled my humans. The algorithm may be temporarily unflappable (as long as the cryptographic algorithms it depends on remain solid), but the implementations of it depend on humans in every step.
