> Project dropped out of the sky on my plate with due date a little too close for comfort. So what do you do?
Obviously, this project wasn't important enough to be given to you with enough time to get it done. Deadlines are often artificial, and this is probably what it was. In the absence of any specifics, I'd say push back on the deadline, negotiate for what you need to deliver something acceptable within a reasonable time, and don't kill yourself for it. If you do kill yourself for this one project, that just sets an expectation for next time that you don't want to have set.
Obviously, this project wasn't important enough to be given to you with enough time to get it done. Deadlines are often artificial, and this is probably what it was. In the absence of any specifics, I'd say push back on the deadline, negotiate for what you need to deliver something acceptable within a reasonable time, and don't kill yourself for it. If you do kill yourself for this one project, that just sets an expectation for next time that you don't want to have set.