Sometimes, it's better to be a little late than it is to drive yourself batty trying to meet unrealistic goals. There are days where you have to have this attitude:"I love deadlines. I like the whooshing sound they make as they fly by." - Douglas Adams
That being said, some deadlines are totally unforgiving. Carefully discern which deadlines are paramount and which are flexible. You'll make your life a lot easier that way.
If it's a choice between turning in the paper late or not turning it in at all, turn in the paper late. As Aragorn says in the book The Lord of the Rings, "Need brooks no delay, yet better late than never."
Show up to work on time. Seriously. People will more readily forgive you when you have a legitimate reason for being late if you usually show up on time. In fact, try to be five minutes early. You'd be surprised just how far that kind of behavior will get you in a job.