Dangerous surpluses

Alan Greenspan and Naomi Klein discuss recent economic history in this interview:

I changed my mind in 2002 and 2003, largely because the whole notion of which fundamentally got me in favor of significant tax cuts without offsetting expenditures was a very special event which probably had not occurred in the United States for 150 years — namely, division of our total federal debt effectively going to zero.

I am sure Mr. Greenspan’s interviews will be popular, but the quote above was in relation to the Bush tax cuts of 2001 and his fear of surpluses.

Could someone explain to me how 6 trillion in debt could be paid down to zero in a short time frame (a decade or two?, eight years?)? He does not mention the mild recession. I believe cactus has a chart somewhere as well, but I will find it later.