I hear this question a surprising number of times when I have initial client consultations. The answer is no. The idea of going to jail for generally failing to pay your creditors is a part of history. Up until the mid-1800's there were debtor's prisons. The development of U.S. Bankruptcy laws and other federal laws during that time helped eliminate the need for debtor's prisons.
Incarceration over debt still occurs. In California, under Penal Code Section 1205, people can choose to go to jail over paying a fine and the time spent in jail reduces the fine. The other way of going to jail indirectly over debt is if you ignore a court order or violate a court order, otherwise known as contempt. The most common violation I see is a failure to appear at a judgment debtor's exam. The judgment debtor's exam is a tool used by creditors that have judgments to determine whether or not there are assets available to pay their judgments. Upon a judgment creditor's request, the court will order a judgment debtor's appearance at the exam. If the debtor does not appear for the examination a bench warrant is issued. Ultimately, if the debtor fails to appear, they could be arrested and theoretically jailed until the debtor complies with the court's order. I have never seen it go this far in any of my cases. I either advise the client to attend the judgment debtor's exam or recommend they file bankruptcy to discharge the underlying judgment.
While jail may not be the likely outcome of ignoring your debts, there are still penalties for failing to pay. Credit score will go down. Creditors can obtain judgments and collect them through wage garnishments and bank levies. Judgment liens can be placed on property. Interest accrues on the debts while they remain unpaid, making the problem grow steadily over time. The longer people wait to deal with unpaid debts the more likely some consequences will be felt.