Well, if I am learning anything in my Master's level Economics course right now, I think that the deal here is the difference between the words "deficit" and "debt". Let's say that the government was carrying a $10 trillion dollar federal debt (total accumulated debt) at the end of Fiscal Year 2008. If, however, the government is able to "balance the budget" in FY09 (um, not likely under BHO, but for the sake of this argument...), and revenue = taxes for the year, then the deficit for FY09 is going to be $0. The federal debt, however, will most definitely NOT be $0 -- it will still be $10 trillion (less any interest paid/accrued).
My $0.02...
If it was balanced from the beginning there would be no debt. The answer they gave was meaningless.