"How can I get the next task done the next day if I'm already behind on everything else? "
In the first place, if you do things right away in the first place you won't be as far behind, because things won't be piling up. Some people feel they don't really want to do anything unless they have a pile of undone things to do, so you have to get yourself out of that mentality. Don't think of the night before the deadline as the time you should be doing something: that is letting the deadline, set by someone else, control your time management instead of having control over it yourself.
I kind of worry sometimes that if I am too quick people (who don't know me well) will think I've been hasty. I've been known to write something, put it in an email draft, and not send it until a few days later, simply so someone won't think that.
If you do have a pile of undone tasks, the first thing to do is to dig yourself out. Once that is done, then you can start doing things as they come up and trying to get yourself to the point where you never have a pile at all. Then, when something comes up, you will have time to do it right then.