Ask your instructor his or her preferences at the beginning of the quarter. Most instructors will tell you what they are looking for in an assignment and what the evaluation criteria will be. If they are not clear about these matters, ask. It's very helpful to know as much as possible about your instructor's expectations before you start your work. Do your best to hit the due date.
University life is a life full of deadlines, so get used to it.
If something serious comes up, let your instructor know immediately. If you get your work back and are surprised by your grade, find out how to improve your work for the next time. Talk to your instructor, listen and learn. However, if you spot what appears to be a grading error, speak up. Sometimes there are scantron errors, sometimes an error might occur when a tired TA is tallying points late at night.