I can imagine someone going to jail for willfully not paying child support when they have income available. If OP gets a job, any job, and gives as much money for his kids as he can afford … I really doubt jail time will be the consequence. But IANAL, and this is not legal advice.
OP said he already asked the judge to amend the order and the judge said he needs to pay up or he'll be found to be in contempt. Based on what I've seen via a in-law, they will throw you in jail if you don't have a job and can't pay. It seems the courts feel like any reduction in income or loss of a job must be intentional and most of them leave the payments the same and say "tough shit, get a job". I guess men aren't allowed to struggle emotionally with the stress of divorce nor are they allowed to be unsuccessful. That in-law basically gave up because you can't get a decent job with a record and there's no way to pay all the back support even if you found a shitty job. And that debt doesn't go away when the child is 18 - it follows you for life.