You can, but only if your economy is growing by 40 billion dollars every month, otherwise it simply dilutes your currency resulting in inflation.
Thing is, all of the US debt is denominated in US dollars, if the dollar halves in value, so does all the cash and savings in the economy, but not only that, so does the debt. Fixed plant, land and buildings however retain an intrinsic productive value.
If you feel, as I have, that the Dollar has been overvalued for some time, then an adjustment is in order. Lower domestic costs will reverse outsourcing and bring production jobs back to the US, reducing unemployment.
Everyone prints money out of "thin air" (or rather paper

) the mandate of most central banks is to ensure that the money supplied into the economy does not significantly outstrip economic growth, if you do, inflation results.