Select a topic. Because you are pressed for time, pick something you already know and care about. Choose a subject that allows you to make as much use of prior knowledge and reading as possible. For example, if you need to choose a literature topic and you know a lot about the Romantic poets, consider choosing John Keats. If you are writing about history and recently read a book about the French Revolution, pick that instead of the Third Crusade. Make sure you have a topic no more than half-way through your first work day.
Research effectively. Read selectively for the information you need to flesh out and defend your thesis and ignore extraneous material. Do not waste time searching bookshelves. Allow Internet searches, bibliographies and encyclopedia entries to point you toward useful sources. Try using book chapters and journal articles rather than whole books, if your topic is small and specific enough. You should complete your research no later than the end of your first day of working.
Make copies of each book page you intend to cite. Take down all necessary bibliographic information and create index cards with your citations on them. This will save you time later because you will not have to track down books you have already returned to the library; if you need a book and someone else has already checked it out, you will have no choice but to locate a different source, costing you valuable time.
Give yourself the entire second day to write your paper. Sit down, begin writing and do not leave your computer until you have composed the entire first draft. This may seem tedious, but if you allow yourself to become distracted even for a few minutes at at time, you may end up wasting hours of time. Write in a straightforward and careful manner. Because you do not have a significant amount of time to devote to revisions, it is better to write your paper well the first time. Progress through the paper in a logical manner from start to finish---do not jump around or skip sections. Take as much time as you need to write the paper, but leave yourself enough time to revise it later.
Take a break from the paper before sitting down to edit it. Take a walk, have lunch, call a friend or read a chapter from the novel you are working on---it doesn't matter what you do, but before settling down for the last lap, you need to refuel. When you finish your break, read your paper aloud to yourself. Check the flow of the argument and note any missteps. With limited time, checking for flow is more important than looking for small stylistic mistakes. Still, you should ensure that the paper contains no obvious errors. Whoever evaluates your paper will struggle to take an argument, even a very good argument, seriously if it is couched in poor grammar, syntax, spelling or punctuation.