Not at all. The interest on the debt is the price of delaying paying for something. We would be no better off if we paid up front. We wouldn't pay the interest on the debt, but, we wouldn't have the $100 billion either, which would be invested in the economy at a higher rater than the low interest rate the fedgov borrows at.
It can work that way. The problem with the Keynsian approach--using deficit spending as an economic stimulus--comes precisely when it stops working because the cost of debt service (interest) itself becomes a drag on the economy.