The best advice I have is to try to stay ahead. My school allows us to log into our classes (which start on Tuesdays) the Friday before class begins. By then, you should already have the book. Begin reading over the weekend, make your introduction and first posts over the weekend. Start responding to classmates as soon as possible. Take online quizzes early. Submit papers a day or so ahead.
Then, if you get called into work unexpectedly, you are already ahead and it won't hurt you. Also, if you are called in and you miss a deadline, communicate with your instructor immediately (even sending an email when you are called in, letting him/her know you'll be running behind on your assignment is helpful). Many professors are somewhat flexible if they know your situation and know you are usually ahead.