Okay, I know officially the answer is "no, there is no such thing as debtors jail for civil debts in the USA", however let's explore this. Suppose a person is sued by a creditor for a debt. Normally what happens of course is there is a court date and eventually you go to court to make your case. Suppose after everything the judge rules you owe $x/month to the creditor(s). Suppose however you can't afford the payment plan of $x/month the court ordered. At this point could you go to jail for failure to oblige the court order?
This is a civil case, taking away your freedom is only for criminal offenses. Not paying your bills is not a criminal offense. It is up to the creditor to look for your assets, etc.
A court can make you show up and answer questions about your assets and income. While you are in court the judge can make you give your gold watch to your creditor.
Outside the parameters of the question there are circumstances like failure to pay child support when you do have the funds that can lead to incarceration. In some places you can be jailed for contempt of court if the court requires your presence to let the creditor have the ability to try to get access to your assets and you do not show up.
The law varies by jurisdiction.
As a matter of U.S. Constitutional law, and under many state constitutional provisions as well, simple non-payment of a debt is not grounds for incarceration, at least if the debtor is unable to pay the debt. At a minimum, to hold someone in contempt of court, they must have willfully disobeyed a court order that they were able to comply with at the time it was disobeyed.
In some jurisdictions, there is some case law supporting the idea that you cannot be jailed for contempt of court based on inability to pay even when you would if income that you could earn was imputed to you. See, e.g., In re Marriage of Sheehan*, 20022COA29 (Colo. App. March 3, 2022). In other words, you must have a present ability to pay to be held in contempt of court.
The U.S. Supreme Court has implied that this is also the case as a matter of federal constitutional law, although, arguably that statement was mere dicta, because a present ability to pay was required in the underlying jurisdiction's law in each of these cases. See Hicks v. Feiock, 485 U.S. 624, 633 (1988) and Turner v. Rogers, 564 U.S. 431 (2011).
But, other jurisdictions distinguish between coercive remedial (or civil) contempt — meaning sanctions that are designed to coerce compliance — and merely compensatory remedial (or civil) contempt — meaning sanctions designed to compensate for losses sustained as a result of the contempt. See, e.g., Spear v. McDermott, 916 P.2d 228, 236-37 (N.M. Ct. App. 1996); see also Falstaff Brewing Corp. v. Miller Brewing Co., 702 F.2d 770, 782 n.7 (9th Cir. 1983). In those jurisdictions, self-induced inability to comply is a defense to coercive sanctions, but not to compensatory sanctions, notwithstanding the U.S. Supreme Court authority cited above.
Another common reason that a debtor may be incarcerated is for failing to provide answers to interrogatories regarding the debtor's assets and sources of income, designed to assist the creditor in collecting those assets, that a court orders the debtor to respond to after a money judgment is entered against the debtor.
A person can be imprisoned with they are found to be in contempt of court, for example RCW 10.01.180 in Washington. The person will not be imprisoned for not paying, they will be incarcerated for willfully refusing to comply with a court order, which means that they have the current ability to pay but refuse to do so. Refusal to pay child support has its own special laws, where there is a stronger obligation to comply with the requirement: you can't simply plead "I don't have any money," you have to prove due diligence in efforts to pay the required maintenance / support. The stick used to enforce those orders is, again, contempt of court proceedings.