First Draft
Do some writing about the project as you go along. Even a paragraph or a page once a week written in your research log will help, restating the position you are taking as your understanding of it changes. Plan to write your first draft early enough to submit it, chapter by chapter, to your adviser and to revise on the basis of his or her comments. Set a deadline to complete a second draft for yourself well before the final due date so that your advisor has time to read it, and you have time to make any further changes that may be needed.
Talking with your adviser after you complete each chapter can help you use the time you have left more effectively. You may discover what it is that you really need to do in order to complete the project in a satisfactory way. You may decide to finish looking into the sources that you have already planned to read. You may decide not to read some of the things you planned to read, but to read something else instead. Or you may decide that you have already read enough, so that what you really need to do with the time you have left is to revise your paper carefully so that it says just exactly what you want to say.
In any case, keep in mind that revising the final product of a research project will probably involve more than just fixing up the style of an essay. You may have to do some more research, write some new sections, or even rethink the whole thing. In the end, the quality of your essay may depend on how much time you have set aside to rework your thoughts for the final draft.