The national debt is actually $86.8 trillion

"The U.S. government's books are in the red by more than $86.8 trillion, according to an influential  University of California San Diego economist (James Hamilton). That's a number more than five times as large as the figure acknowledged by the U.S. Treasury and used by government agencies to justify their budgets and spending."
Read more: http://www.dailymail.co.uk/news/article-2380987/Leading-economist-says-US-national-debt-actually-86-8TRILLION.html

The details are in a paper entitled "Off-Balance-Sheet Federal Liabilities".

I don't know where the $86.8 trillion comes from, since the calculation shows $70 trillion as of the end of 2012.