You email your teacher immediately and he is able to see you tomorrow. You make it to the appointment and lay the cards on the table. You tell him how stressed you feel, how you need to do well, and how you can't get started. Surprisingly, he doesn't seem to think that you're stupid! He points you in the direction of a couple of books and a couple of websites. He also tells you of some of the common issues that students have with this paper and tells you to feel free to come and see him any time if you're having trouble.
You head off, get your hands on the material that he suggested and start reading. Things seem to get clearer. You're still not a fan of this essay topic, but at least you feel like you are starting to understand it. You do some further research, take some more notes and get to a point where you can cobble together an outline. From here the essay isn't too hard to write. After proof-reading it and making some edits, you feel like you've done a decent enough job of this and hand it in. You're not sure if it is your best work, but you somehow think it will be allright. At the very least, you know that your teacher is a pretty good guy who is willing to help you out!
This student was wise enough to bite the bullet and ask for help. Hopefully there are also structures in place for the teacher to recognize when students are having issues. Class check-ins, inquiry journals, learning logs or some other reflective mechanism might also be useful for this purpose.