In his work, "What is the Dollar in the United States" (online), its author, Dan Goodman, shows that the Continental Congress established the dollar, as a coin, containing containing 375.64 grains of fine silver, equivalent to the then current Spanish Milled Dollar coin. The United States Congress completed the work of the Continental Congress by establishing a mint to coin the dollar (and parts thereof). However, the dollar was defined to be a coin, containing 371.25 grains of fine silver, equivalent to the then current Spanish Milled Dollar coin. The reason for the change in the number of grains of fine silver, was, according to Alexander Hamilton, in his report of the establishment of a Mint (Jaunuary 28 1791), that "[t]he dollar originally contemplated in the money transactions of this country, by successive diminutions of its weight and fineness (by the country of Spain), has sustained a depreciation of five per cent. . . . This, nevertheless, is the condition of one which, having no coins of its own, adopts with implicit confidence those of other countries."

So, though money under the Constitution may not include gold or silver coin, a dollar, however, is under the Constitution a silver coin containing 371.25 grains of fine silver. And since debts are generally denominated in terms of dollars, then only silver coin (and maybe gold coin) can be tender in payment of the debt.

On the issue of legal tender:

The United States cannot make its obligations a legal tender in payment of private debts. In the case of Julliard v. Greenman, the United States Supreme Court held that: 1) Congress had the power to make its obligations a legal tender in the payment of private debts, and 2) that this power was an implied power under the Constitution based on the case of McCulloch v. State of Maryland. The Court determined that this implied power of making the obligations of the United States a legal tender in payment of private debts was a means (incident) to the power (expressly) given to Congress to borrow money on the credit of the United States.

However, the case of McCulloch v. State of Maryland was wrongly decided. The concept of implied powers does not exist in the Constitution. In fact, such a concept, if a doctrine would be in conflict with the doctrine that the Congress is a government of enumerated powers. As such, Congress does not have the power to make its obligations a legal tender in payment of debts, since the concept of implied powers does not exist in the Constitution. Since the power is not granted (expressly) to Congress, the power to make its obligations a legal tender in payment of private debts is not given to Congress under the Constitution of the United States. This is shown in the work, "The United States government does not have the power to make its obligations a legal tender" (online) by Dan Goodman.