Of course crying it out won't work. Why would it? She doesn't understand when you abruptly change the sweet wonderful routine of holding and nursing her to sleep. She is going thru a major change-teeth and growth spurt! Poor kid! She is relying on the one thing she knows will give her comfort. It's not like she can say "Mother, I'm feeling cranky and uncomfortable. Can I have a tylenol and a long hot bath to feel better?" She *knows* nursing will help her feel better. It's instinctive and ingrained. And you say it's only recently begun. As a breastfeeding mama you know when they start something like multiple nursing it's because they need it-growth spurt, teething, etc. And you know it doesn't last long.
Now is not the time to wean. You will get that response I'm sure. Most people don't nurse past 6 months. They have no understanding of extending nursing and the dynamics. Weaning her while she needs you to help her thru this transition isn't the best idea.
Don't leave her to cry-she doesn't have a clue what to do when you just leave her, don't try to wean her while she is going thru such big changes. I agree with Tonya C. Tuck her in bed with you and you'll all get some sleep. As soon as you see she is getting thru this you won't need to put her in bed with you in the middle of the night.
I highly recommend checking out Dr. Sears sleep book for toddlers and the Baby Whisperer for toddlers. It will give you valuable info on how to teach the little ones to sleep.
Also, my daughter didn't sleep well thru the night until I weaned her at 20 months and even now she isn't as good a sleep as my son was/is (he was weaned at 16 months). Some kids are just better sleepers than others but they have to be taught how to sleep.
This too shall pass Mom!