I am not expert on the subject of lincoln or of green backs. However, my understanding is that he needed more money to slaughter more southern patriots and the interest rate the banks were going to charge him on his bonds was too rich for his tastes. Killing must be done cost effectively, you know.
So it is the same story with every war. Government needs money so government creates new money out of thin air. Greenbacks are the most obvious ones in history. He just had money printed up and forced people to use it.
no coin clipping, no fuss, just print and here you go!