The colonies issued their own currency before the Currency Act of 1764 required only hard specie to please the Bank of England. The colonies were doing economically well, but this deflationary act sent them into a depression. Ben Franklin at the time endorsed the sovereign colonial monetary system, and would argue that the Currency Act of 1764 was the prime reason for the War of Independence.
Printing money for a handout or a war is obviously going to devalue the currency, but if the government issues printed money into something associated with production, the added currency is immediately backed by that production. It's a little abstract, but the goal would be to create new money in terms of economic growth, so the amount of money is always proportional to the amount of wealth.
And there's no reason why a republic couldn't monitor this system effectively, and for once, the central government wouldn't be beholden to the banking power. We will never be a sovereign people without the power to issue our own currency.