You have no idea how state, county, and city governments work in the US do you? None of those entities can print money. Those parts of government raise money through taxes.
Only the Federal Reserve can print money. The way the rest of the federal government besides the Fed gets money is through taxes and by selling treasury bills and bonds where they promise to pay back the money with interest. Other parts of government can also sell bonds.
If entities believe that a government is running the printing presses there is a currency run and inflation. Ever wonder why assets inflated tremendously the last 8 months relative to the dollar? Ever wonder why the dollar has lost 10% versus other currencies? Things that are fixed in price just got cheaper (like fixed rate mortgages). Things that aren’t, have gone up in price (restaurants, produce, lumber).
Also the running of the presses may add money to the Federal government but may hurt some local governments in the same manner. For example, a city in California dependent on property taxes may have trouble paying its bills when there is a lot of inflation. That is because Prop 13 mandates no more than a 2% increase in property taxes per year. Those private companies that it gets services from will bid at higher prices.