I would add the following: If there had been a federal government, then that government would not even have had to do anything that looked like "printing money" in public discourse.
This is because this federal government would not have had any trouble issuing new debt in the form of bonds. Why not? Because everybody would have known that the European Central Bank would effectively guarantee those bonds under any condition, and therefore there would not have been a panic about the debt in the first place. It's all a psychological game.
As evidence, consider that the fiscal policy part of the US federal government has not done anything that looks like "printing money" up to this point. All they have done is issue bonds, i.e. get loans from creditors.
Yes, the Fed has done things that look like "printing money", but that's monetary policy which has nothing to do with social safety nets.