If you call the district court on Monday and explain...you might be able to get away with no extra fines and no warrants. I had this happen to me once with a parking ticket, and just had to pay the fine in full when I called in. My penalty was that they wouldn't allow payment arrangements. But who knows? It all depends on the person taking the call.
I don't think you'd get put in jail right away. Monday morning, they'd just be getting the list of offenders who didn't pay on Friday and POSSIBLY issuing bench warrants, if you call FIRST THING Monday morning right when they open, you can probably get it squared away!