The former central bank leader — nicknamed "The Maestro" by his supporters — said he worries the current economy could be heading on a path similar to 1979, when the 10-year Treasury note was yielding around 9 percent before surging dramatically, gaining 4 percentage points in just a few months.

"I listen to a lot of what people say that we don't have to worry. We can do it in our own time," Greenspan said in regard to trying to bring down Washington's $1.2 trillion budget gap. "Good luck. The markets have not been told this."

With the economy slowing and the benchmark government note yielding just above 1.50 percent, inflation is hardly a hot topic in the market.

But Greenspan said he worries that economists lack a sense of urgency about getting the deficit spiral under control. Without fiscal discipline, the market can push rates higher rapidly if confidence wanes in the government's ability to get a handle on the problem.