The US National Debt is held in T-Bonds (Treasury Bonds) as the video discusses. If we reduced Government spending to less then the Tax Revenue, then the Surplus each year could be used to purchase back the T-Bonds, thus lowering the National Debt. Or could be held to fund next years governmental spending so new T-Bonds would not need to be issued.
Could this be done over night? No. But over time (10, 15, 30 years)? sure.
Of course, this brings up a major issue - If 16 Trillion isn't being held in T-Bonds and is pushed back out into the Markets, suddenly the value of circulating dollars would drop. This would probably be a bigger problem then the National Debt.