Help! Our new kitten won't use her litter box!?

Every cat I have ever owned has learned to use her litter box within a day or two. This new kitten refuses to use her nice, roomy litter box with fresh litter. It's so frustrating because she is going everywhere in the house, including my bed! I keep showing her the box and trying to get her to use it, but she won't. I am so grossed out and upset. Putting her outside is not a n option since it's dangerous for her. Has anyone else had this problem before? I thought cats were instinctively drawn to litter bboxes. Someone please tell me there is an end in sight to this. I can't handle this!