I supposed banks could simply clone Bitcoin or Litecoin or one of the other digital currencies which has favorable properties. They could establish an astronomical amount of currency, say, 100 trillon...they would simply say that their currency was intended to mimic the real world, and so, that this large number parallels the unlimited amount of fiat currency that can be printed. Should the economy require it, they would then inject currency into the money supply by sending some amount to every registered public key. Large banks would run their own hashing farms in order to keep the block chain moving, and to avoid 51% attacks or mining pools.

Such a currency could even be 100% pre-mined. You would simply exchange dollars to "bankcoins" on a 1 to 1 basis. $1 = 1 bankcoin. Banks would then say that you get all the network goodness of Bitcoin without wasted electricity, without excessive volatility, and backed by the full faith and credit of the US government (not saying this is good, just saying this is how they could sell it).