The United States Constitution demands that the United States of America have a gold standard. Article I section 8 clause 5 states that Congress has been granted the power to "coin money, regulate the value thereof, and of foreign coin, and fix the standard of weights and measures." Article I section 10 clause 1 states that "No state shall make anything but gold and silver coin a tender in payment of debts."
There is no mentioning of the approval of a paper currency within the United States Constitution to be a legal tender for all debts, public and private. Only gold and silver is mentioned as a legal tender for all debts.