Actually, the Federal government *doesn't* have the power (never a right) to print money. It has the power to coin
money and regulate it's value. Crucial difference in the wording.
A dollar bill is merely a bill of credit; something expressly forbidden to the States due to the problems it causes (which we're seeing today).
Coining money means literally that; stamping and regulating coins. "Money" has intrinsic value, whereas a bill is merely a piece of paper.
Scope the antifederalist papers #44 to see the concern
11. Though I believe it is not generally so understood, yet certain it is, that Congress may emit paper money, and even make it a legal tender throughout the United States; and, what is still worse, may, after it shall have depreciated in the hands of the people, call it in by taxes, at any rate of depreciation (compared with gold and silver) which they may think proper. For though no state can emit bills of credit, or pass any law impairing the obligation of contracts, yet the Congress themselves are under no constitutional restraints on these points.
And the Federalist response #44
The extension of the prohibition to bills of credit must give pleasure to every citizen, in proportion to his love of justice and his knowledge of the true springs of public prosperity. The loss which America has sustained since the peace, from the pestilent effects of paper money on the necessary confidence between man and man, on the necessary confidence in the public councils, on the industry and morals of the people, and on the character of republican government, constitutes an enormous debt against the States chargeable with this unadvised measure, which must long remain unsatisfied; or rather an accumulation of guilt, which can be expiated no otherwise than by a voluntary sacrifice on the altar of justice, of the power which has been the instrument of it. In addition to these persuasive considerations, it may be observed, that the same reasons which show the necessity of denying to the States the power of regulating coin, prove with equal force that they ought not to be at liberty to substitute a paper medium in the place of coin. Had every State a right to regulate the value of its coin, there might be as many different currencies as States, and thus the intercourse among them would be impeded; retrospective alterations in its value might be made, and thus the citizens of other States be injured, and animosities be kindled among the States themselves. The subjects of foreign powers might suffer from the same cause, and hence the Union be discredited and embroiled by the indiscretion of a single member. No one of these mischiefs is less incident to a power in the States to emit paper money, than to coin gold or silver. The power to make any thing but gold and silver a tender in payment of debts, is withdrawn from the States, on the same principle with that of issuing a paper currency.
As you can see, both sides were agreed on this point.