Then you would have excess money supply, and if demand for the currency stays the same, it will devalue the currency, which causes inflation. That might be OK, as long as its below your economic growth rate.

With the US, the treasury uses the fact that the US dollar is one of the reserve currencies (the euro is catching up), and the US government demands payment for their security services to Japan/Korea/etc in USD, etc,etc helping maintain the demand for the USD.