If we actually have any Gold left I believe we would be unwise to use it to pay off the National Debt, Gold is the only thing that actually has any real value and once it belongs to others including other Countries we are screwed.
That is unless the United States does what I would suggest and that is replace Gold with Uranium or more correctly with what we use Uranium for and we have the most of anyone else, Thermonuclear Warheads. And I don't mean selling the Nukes but using the threat of using them to get anything the United States Needs.
Think about it, if need oil and no one will sell us any without receiving something of real value, meaning Gold or Money backed by Gold and we no longer have any Gold how can we get the oil.