Ooooooooooh I know this type! I always try to remind myself that when someone is that nasty, it's probably because they've been dealt a really bad hand in life. Usually the people who are overly critical, are people who have ben criticized a lot in their lives. I know that she is an adult, and it's not an excuse, but some people never know better until someone teaches them, or shows them that there is a different way of living. I mean, look at the way she made you feel, and want to react. She probably gets that a lot, and probably has for most of her life. Her perception of the world is a very negative one, meaning she probably had a lot of negative things happen to her AND because of that her pain and unhappiness breeds even more negativity for her.
Have you ever tried to talk to her? I doubt you can change her, but maybe she just needs a friend. That way, maybe she would become loyal to you, rather than trying to make you look bad at work.
I would definitely say something to her, though. I would start like the others said, by asking "I hear you have a problem with my work...", she how she responds, and then say "look, I know that you've been stressed out, but that is no excuse to try to give me a bad reputation at work. I have kids I need to feed, and with the economy the way it is today, I would ask you to reconsider making your false statements that could potentially affect my employment. That is, unless you would be able to sleep at night knowing that you took the food from my children's mouths if I were to lose this job because of accusations that you've made".
I also agree that you should talk to your boss about this, because you can't risk your job. I've learned the hard way that keeping my mouth shut in the workplace, and just hoping that the boss is smart enough to catch on to what's really going on, is like trying to wish yourself thin. It's just not going to happen, you have to do something.