The thing is: paying off the national debt would raise GDP by a factor of 3–4 times the amount spent on interest on the national debt(Pew put that at $222 Billion/year in 2013 5 facts about the national debt: What you should know), which would be roughly a sustained 5% increase in GDP beyond other expected growth. read more
So the end of debt would mean the end of Treasury bonds. But the U.S. has been issuing bonds for so long, and the bonds are seen as so safe, that much of the world has come to depend on them. The U.S. Treasury bond is a pillar of the global economy. read more