Approximately 10% of the federal debt of the United States is in the form of Treasury Bonds given to the Federal Reserve to back the printing of Federal Reserve Notes. Thus, each dollar circulating in the form of a Federal Reserve Note represents one dollar in unnecessary debt held by the government.
United States Notes, on the other hand, are issued directly by the Treasury and are a true fiat currency, being backed only by worldwide confidence in the government. Each dollar circulating as a US Note represents an increase in the money supply, not an increase in debt.
Due to the increase in money supply, a consequence would be an increase in inflation, but as paper money represents only a tiny fraction of the overall money supply, direct effects would be balanced by the decrease in debt.