Bitcoin's backing stems from its cryptography, which prevents the arbitrary replication of coins, along with its other properties that allow it to act as a good medium of exchange. Similarly, gold's "backing" stems from its scarcity, and other physical properties, that make it suitable to act as a money. If gold could be arbitrarily replicated or if its scarcity was similar to iron, gold would cease to be a good money. Thus, it is totally pointless to back Bitcoins with anything because Bitcoins already have value due to the fundamental properties they possess. They don't need backing like paper because paper can be easily replicated. Initially paper currencies were nothing more than warehouse receipts for gold bullion. People traded the receipts as if they were gold because they could be redeemed for gold at any time.
Think about what would happen if a Bitcoin represented some fixed amount of gold. For each ounce of gold a person places into a bank, that bank would then issue that person one Bitcoin. Obviously this presents a radically different system than the present Bitcoin system, and one that is completely unnecessary anyways. The gold held by the bank would simply sit in the vault unused for any other purpose; it would become a wasted resource.
The purpose of a gold backed currency is to prevent arbitrary inflation of the money supply. In fact, the U.S. could emulate a gold standard WITHOUT any gold by simply creating a monetary system where the number of dollars in circulation is set to a fixed limit. Setting a fixed limit of dollars would achieve the same economic results as if the country was operating on a gold standard, yet the banks wouldn't need to hold any gold at all.
Bitcoin is the best of paper currencies, electronic currencies, and the gold standard all rolled into one. Bitcoin eliminates the need for backing, allows for online transactions, is easy to store and carry, eliminates the need for banks/government to issue the currency, and retains the same anonymity as physical currencies.