Puritans first issued paper bills because they owed Britain money to fund their war against France. The Civil War required even more:
To foot the bill of the Union Army's campaign, the government had to issue $450 million in greenbacks (about $8.1 billion in 2011 dollars). They may have been un-constitutional, but they worked, making it possible to buy equipment and pay soldiers. War has a habit of quieting concerns about currency's backing.
The end of the war, however, brought with it inflation and renewed attention to the constitutionality of paper money. It was Salmon P. Chase who, first as the secretary of the Treasury Department, made the greenbacks possible. Then, as a Supreme Court justice less than a decade later, he made one of history's most famous flip-flops, ruling that currency notes were illegal. He made this determination despite the fact that the face printed on them was none other than his own.