Fiat money is not itself a debt instrument. Debt comes into existence when one party, the lender, loans money to another party, the borrower. The debt instrument is the borrower’s I.O.U. to pay back the principle borrowed plus interest. U.S. Treasury securities are debt instruments. Corporate bonds are debt instruments. Certificates of deposit are debt instruments.
Fiat money is money itself. It is not itself a loan to a borrower that the government must pay back principle plus interest in the future. Just like a counterfeit bills are not an I.O.U. of the counterfeiter to pay back principle plus interest in the future to someone.
Governments of some countries can, and have in the past, simply printed fiat money and spent it to buy goods and services. Technically, this process need not involve debt at all.
In practice the Federal Reserve’s policy of issuing of fiat money expands the supply of credit and thereby makes the sale of federal debt by the Treasury more feasible. Without monetary inflation and credit expansion interest rates would be much higher and government borrowing less feasible.
Instead of a balanced budget amendment, a more binding constraint on the issue of debt by the federal government would be to supplant the Federal Reserve with a commodity money like gold coins or silver coins.
In the first chart at the link below is the history of Gross Public Debt. You can see how it exploded after the U.S. repudiated dollar redemption into gold in 1971.
You can read about the issues involved in Murray Rothbard’s book, What Has Government Done to Our Money?