I have this too, actually, though I know I am a fine tank. the spotlight position, where I determine pace, speed, and am basically either keeping the group safe or not is really stressful, even though it never really goes 'wrong'.
I love tanking, but this stops me from rerolling. As a healer I feel much safer - you're doing a great job if nobody notices you and that's exactly what i like. Plus, I know exactly what I'm capable of, and not, and fails and good stuff are much faster apparent than when I'm tanking. As a result, I know right away when I could have played better, or did an excellent job - I'm not always scratching my head wondering what others think of my performance, since, if I'm any good, nobody will even know I'm there.
as a dps I feel in the middle, meter competition, where on my main I'm doing fine on, is a constant stress struggle for me on alts, which is why I don't usually have any dps alts. I can't pull the same numbers on an alt (lfr gear at best) as I do on my main (hc raid gear) and that frustrates me, and it makes me feel 'bad'. I know it's completely irrational, much like 'tanking-nerves'.
Hope you feel less alone in your tanking nerves now, and that you learn to deal with it!