I'd also consider going public in such a situation. Companies hate when dissatisfied customers speak out. I'd blog about it, if I had one, and I would call my local TV news station's consumer reporter and relay your story. My goal would be to get a full refund, and then I'd go out and get a different machine. I wouldn't hesitate to mention to the CEO exactly what you expect from them. I also might mention going to your state's attorney general's office for relief and if I didn't get satisfaction, I would do it.
I don't know anything about Singer but I know that lemons do occur in sewing machine manufacturing and they need to stand behind their products.