I see a lot of people misunderstanding the topic at hand...
Some are talking as if more notes must be printed for FRB to work. Others are talking about it as if bitcoin would be what backs the notes. This isn't the case as the only "notes" that would be used are those of the account holder. Essentially, that's just a login stating that you own the account with the bank. In this case, the bitcoins wouldn't be stored, they would be what's given out as the notes. If it's gold you're talking about, think of it as holding an account with the bank, but the gold is lent out. That's the form that bitcoin FRB would have to take to work.
Others look at history and say that, eventually, all FRB schemes fail without government intervention without analyzing the causes for that failure. Most cases have government intervention in the loanable funds market in some way, such as the manipulation of the money supply or interest rates (monetary manipulation,) or problems with moral hazard (FDIC, etc.) Sans that manipulation, manipulation which is either extremely difficult or impossible to create in the bitcoin economy, such systems have existed and have created stability.
Others still seem to think that the only way for FRB to exist with bitcoin is for it to be melded into the current financial structure, but that's certainly not the case. What will most likely happen is that wallet services will become the more secure and more useful provider of funds management. For example, someone will most likely create a bitcoin based debit card or phone app that must work through their system (much like VISA for debit cards working through your bank account,) in which case there's reason to believe that others will create competing systems. Through this process, a depository system will be constructed in which interest rates will become a competing factor -- this will require a fractional reserve system, or deposits that aren't 100% on demand. The competing process here will set reserve rates as opposed to interest rates.
Hopefully this is helpful to those who have responded.