This is my first time playing an MMO, so it is of course the first time I've played a healer, but what I've noticed is that it feels very much like playing a goalie. You're the last line of defense and the easiest one to blame, but it's a team effort.
It's really easy for me to tell when I'm going to have problems, though. If I spend the first 30 seconds of a battle having to heal everyone, I can tell it's going to be bad. Usually, the first couple battles in a group instance are easy enough, though, that we can power through it and I can course-correct.