As you no doubt know, debt used to be a crime punishable by imprisonment and other measures. The first inklings of change started to happen as early industrialization took hold; to engage in industrial efforts, capital needed to be accumulated in large amounts, and the easiest way to shuffle capital around is through debt. However, you could still be imprisoned for defaulting, which made no sense because they were also held accountable for the charges accrued while holding them, while unable to work to pay off the debt. The US stopped using federal law to imprison debtors in 1833, leaving it to states to determine individual action.
In my opinion, the interesting stuff happens in the twentieth century. It is only in the time of the New Deal that, through encouraging federal rulings and financial legislature, it becomes socially acceptable, fairly common and definitely profitable (for banks) for Americans to have debt. This was in keeping with Keynesian economics, which dictated that by encouraging spending (even of borrowed money) the surplus of material goods could be used up, and America would no longer be drowning in gluts of worthless corn and other products. In World War II, revolving credit was created to help control inflation. In the postwar world is when credit (monthly, normalized debt) became standard practice for avidly consuming Americans, buying goods and products of all sorts to outfit their tidy new suburban homes (also paid for through debt.) Only in the 1970s does going into debt stop making sense as the economy tanks and stagflation sets in; at the same time, Americans are using modern credit cards widely and perpetuating an industry of money-making out of debt.
Louis Hyman describes the initial 'financial revolution' really well on his opening page :
While personal lending had always existed, before 1917 it had never been legal to charge interest rates high enough to turn a profit and, equally important, lenders had never been able to resell their customers' debts or borrow against them. In short, personal debt had never been able to be a normal business. [...] By the end of the twentieth century, however, such petty loans to workers had become one of American capitalism's most significant products, extracted and traded as if debt were just another commodity, as real as steel.
And also:
For borrowers, the fungibility of money meant that one form of debt could be paid off with another, The modern debt regime relied on this convertibility, not only to transform installment contracts into personal loans or credit card debts into home equity plans, but to turn the wages of labor into debt repayment as well. [...] For lenders, transforming capital into debt was the essence of their business.
Louis Hyman, Debtor Nation: The History of America in Red Ink (Princeton, N.J.: Princeton University Press, 2011).
EDIT: Something Hyman doesn't dwell on but I think is well worth pondering is that the U.S. government itself paved the way for American consumer debt by example in the crucial period of World War I that he cites. Debt was acceptable, even instrumental to achieving one's goals, because the United States government was deep in it, too! As detailed in Julia Ott's study of American stock-owning practices,
Policymakers looked upon mass investment in federal war debt as a means of encouraging a widespread sense of identity with the war effort and the nation itself [...] even for those lacking full political rights. [... at a time when] Americans grappled with the very definition of citizenship. [...] Investment both made and manifested citizenship, as the citizen-investor assumed full membership in the polity with his or her acquisition of war debt.
Julia C Ott, When Wall Street Met Main Street: The Quest for an Investors’ Democracy (Cambridge, Mass.: Harvard University Press, 2011).[Sorry to butcher it, but I didn't want to type the whole page up]