Fiscal positions are flows; debts are stocks (net fiscal positions accrued over time). The last time the US paid off all of its debt, the country went into recession. Someone's debt is someone else's savings. The gov debt = nongov sector savings; nongov sector = domestic private sector + foreign sector.
As far as I know, 'they' contemplated that the FED might buy private sector IOUs in order to expand the money supply and keep the economy going - which would be quite the socialist move

Anyway, they would have never been able to eliminate all the government debt. I dislike the expression "pay off the government debt" because it pertains to outdated logic and it doesn't make any sense. Government debt = nongov sector assets. "Let's pay off our savings", that doesn't make any sense.
Returning to the point of debt, all their musings about how to change monetary policy and what not for a post-government debt epoch shows just how delusional Clinton's staff were - for they were totally clueless about the automatic fiscal stabilizers.
They would have been faced with a recession, which they were, the moment in which the domestic private sector's credit would go dry - the foreign sector was in a net surplus against the US anyway - thus higher savings desires and lower spending desire and capacity would have changed the government's net fiscal position dramatically. In order to retain perma budget surpluses, the US federal gov would have required to take active pro-cyclical fiscal measure - aka higher taxes and lower spending. Something which would have been extremely hard politically and socially to do. We've seen how bad life is on the grass during private debt deleveraging periods and with too small deficits on top of that - let alone budget surpluses.
One more point that the authors of the paper were talking out of their ass is the very beginning of their paper:
The financial services industry has grown tremendously in this country over the past eight years, and done a very good job of handling growth and the increased risks that accompany it. The industry accomplishes this task most fundamentally by separating risks by type, making them easier to evaluate and price.
LOL!