Schedule a meeting and ask for her feedback on your work performance. Assume she has personal problems and ask others if they are aware of details. Begin working on your resume. You would rather quit than be fired. You've just found out that you are the target of a nasty rumor at work.
Rumors have a way of blowing over eventually.
Make it a point to find the source of the rumor and confront him or her aggressively. Create a rumor about someone else to take the spotlight off yourself. Become depressed and distracted. It's obvious your talents are not appreciated where you are. Resolve to make life difficult for the co-worker.