Quick side note: That figure is some $5.595 trillion higher than the $10.627 trillion it was back on 20 January 2009, when Barack Obama was sworn into office.
To answer the question, we've updated our tool for converting cash into an equivalent value in gold! Now, in addition to figuring out how big a solid gold cube would have to be to correspond to a given amount of gold at current spot market prices, it will now figure out how many standard 20-feet long by 8.5 feet wide by 8.0 feet tall intermodal shipping containers would need to used to transport the gold to all the people to whom the government owes all that government-issued debt!
What we find when we plug in the numbers as of 1 November 2012 is that the entire national debt of the United States is the equivalent of a solid gold cube that is nearly 80 feet tall by 80 feet long by 80 feet wide. Transporting all that gold would require over 431 of those standard 20-foot long intermodal shipping containers.
The only problem with that is that all of the gold that has ever been mined on Planet Earth would only make a solid gold cube that is 66.1 feet high by 66.1 feet long by 66.1 feet wide, which would work out to fill just over 249 of those 20-foot standard shipping containers. Even if Fort Knox held all the gold in the world, the U.S. Treasury would still be more than 182 shipping containers short of being able to pay off the national debt in gold at today's spot prices.
President Obama's contribution of $5,595 billion to the U.S. national debt during his term in office through 1 November 2012 would be represented by a solid gold cube that is 55.7 feet high by 55.7 feet long by 55.7 feet wide, which would represent about 60% of all the gold that is known to exist in the world. It would take just over 149 standard shipping containers to hold all that gold if each container were completely filled with no air gaps.
Laid out end to end, those 149 standard shipping containers would be almost six-tenths of a mile in length. That's just over one-third of the length of the 431.5 shipping containers that would hold all the gold representing the United States' entire public debt outstanding.