How can they get me for back child support if at the time I had no sort of income?

Once a child support order has been issued by the Court, you are required to make monthly payments in the set amount until such time as the order is modified or the child support obligation is terminated.  If, for example, you are ordered to make monthly child support payments in the amount of $950.00, and you subsequently become unemployed, your monthly child support obligation will continue to accrue at $950.00 per month, unless you have the child support modified (reduced) through the court.  It is your responsibility to file or retain the services of an attorney (best option) to file for a modification of child support.