"We've got to resolve this issue," Greenspan said of the ballooning U.S. debt levels.
He spoke about the issue as a panel, chaired by former White House chief of staff Erskine Bowles and former U.S. Senator Alan Simpson, is due to deliver a report on debt and deficits by Dec. 1.
A draft report made public last week offered a series of politically tough tax and spending choices that would seek to reduce the debt by $4 trillion by 2020.
The report received a lukewarm reception from some politicians and outright condemnation by others, including House of Representatives Speaker Nancy Pelosi, who pronounced the ideas "simply unacceptable."
Greenspan, who spoke on NBC's "Meet the Press," said he believed "something equivalent to what Bowles and Simpson put out is going to be approved by Congress. But the only question
is whether it is before or after a crisis in the bond market."
He said the risk is that the deficit, which hit $1.3 trillion this year, could spook the bond market. That would result in long-term interest rates moving up rapidly and could lead to a double-dip recession.