Can my driver’s license be taken away for back child support?

My ex is threatening me that she will get the Los Angeles Dept. of Child Support to take away my driver’s license if I don’t pay all of the back child support I owe. I am a truck driver and have a CDL license. I’ve been paying what I can toward the back support but I can’t pay it all at once. It doesn’t make sense that the child support office would take away my license when that means I would lose my job. If I can’t work my ex has even less chance of getting any child support. Can LA child support services take away my driver’s license for unpaid back support, even if I am making payments toward it?