Whilst the method dstiles suggests may be a longer process than editing on live. I would certainly hesitate in editing live code directly. You are effectively testing your changes in the live environment. You don't say what your situation is, working on your own sites, managing sites for others, etc. But whatever the situation you are leaving yourself open to a whole world of pain if you get something wrong.
I've worked for in web dev for quite a while and as a developer for others, I'm usually not even allowed near live servers let alone be able to update anything on them.
Anyway back to your query though. I occasionally use FileZilla to view files on my servers. I believe you can edit them through this with just the one login to start the session.