Almost from the beginning of American history Americans have relied on paper money. Indeed, the Massachusetts Bay Colony in 1690 was the first government in the Western world to print paper currency in order to pay its debts. Although this paper money was not redeemable in specie, the Massachusetts government did accept it in payment for taxes. Because Americans were always severely short of gold and silver, the commercial benefits of such paper soon became obvious. Not only the thirteen British colonies, but following the Revolution the new states and the Continental Congress all came to rely on the printing of paper money to pay most of their bills.
The government has men with guns and dungeons. The armed men will throw you in the dungeon unless you pay taxes. So if the government chooses to accept random pieces of paper as payment, the pieces of paper become valuable. The point of collecting taxes isn't that the government needs money (it can print money) it's that if the quantity of taxes is too low relative to the stock of money, then the money loses its value and the price level rises.