What this all comes down to is the issue of contempt of court. In theory at least, we live in a nation of laws, and rely upon the courts and judicial system to enforce those laws. In order to enforce the laws, a court issues orders. Personally, I issue dozens of orders every day, from the mundane (order a person to complete a court appointed attorney application or take a drug test) to the extreme (terminate parental rights, incarceration, or on a good day grant an adoption). What happens when those orders are ignored? The judge/magistrate should sit on his hands and do nothing? No, the order must be enforced. And, the way an order is enforced is a contempt action.
There are two kinds of contempt. Direct contempt, like where the defendant picks up a pad of paper and throws it at the judge, or tells the judge to *expletive deleted*ck himself, or something else done in the court which interferes with the court's ability to conduct business. In direct contempt, the court can act summarily, meaning there is no right to trial or such, the judge issues an immediate order for punishment, be it fines or incarceration.
Indirect cintempt is what is being talked about with child support. In other words, the court issues an order, and someone fails to comply with the order. it is enforced differently. The contemptor has rights to a hearing, to counsel, to appeal, etc. More importantly, the contemptor has the right, even after being found in contempt of court, to purge the contempt by complying with the original order. this is before punishment is imposed. In other words, you get a second chance.
Now, while we most often hear about the support cases, indrect contempt actions occur all of the time. We see at least one a week around here. They vary from case to case. Often in divorce cases with children, we see contempt actions brought because the child was brought home from a visitation late, or picked up late, etc. in civil cases, we see contempt actions brought because discovery is late, or one party misses a deposition, or doesn't deliver something on time, etc. the reason you don't here more about these is that the contempt is genrally purged, and no one goes to jail. or, the judge/magistrate sees the action is garbage and treats it as such.
In child support contempt, the court issues an order. Here in Ohio, child support is determined based upon a standar set of figures the legislature adopted as standard guidelines. Where one falls on the guidelines is based upon level of income of both parents. the law allows for a judge/magistrate to order a deviation for good cause shown, such as in hardship situations, disability, etc.
So, the order is made after a hearing to determine what the amount should be. Obligor (the person who is supposed to pay) doesn't pay. A contempt action is brought by Child Support Enforcement Administration. A hearing is held, and the judge or magistrate must determine of the obligor is in substantial compliance with the original order. If yes, case dismissed. If no, then the obligor is in conntempt. A sentence is rendered, depending upon what number contempt the case is (1 - 30 days, 2- 60, 3- 90, 4 -120, 5- 150, 6-180, etc.). the sentence is rendered, and then the person is ordered to purge himself of contempt by paying, and a review is set. if in compliance, the contempt can be dismissed. If in partial comliance, the case can be set for further review.. If the obligor is not in substantial compliance at the time of the review, all or a portion of the orgininal sentence may be imposed.
Now, rabbi, you asked what authority the Court has to jail someone for failing to pay an obligation to another party. the authority falls from the failure to comply with the court's order, not the failure of payment necessarily. But, as a matter of argument, I have seen a person jailed for failing to pay a civil judgment after an amount had been ordered. how else can a court enforce its orders. And, when a court stops enforcing its orders, well, I think we call that TSHTF around here.