BRF, I hate to admit this, but I went years of fishing in the park without catching anything...yes I said: YEARS!!
I could go down to the Hiwassee and catch fish, I could catch fish in Colorado, but I had the darnedest time catching fish in the Smokies. From about 1999-2006 I fished up to about half a dozen times a year in the park and never caught a fish. I mean NOTHING!
Then I went fishing with Hugh Hartsell last year and it all changed. Its much different fishing in a tailwater than in the mountains, and I had not really fully grasped what that meant. Like everyone has already said, you have to be sneaky and quiet (no backcasts, no standing, no....). Once I really started focusing on that, I started to catch fish. Not big numbers at first, but I stopped getting skunked. As the year wore on I started getting the hang of it and got to the point of catching 20-30 fish each day (not the numbers that some of the regulars catch, but a fair amount of fun for an outing, and enough for me to be happy about my effort). I still have a lot to learn, and there are still lots of days that I only catch 3 or 4, but it takes time and persistence for these streams to give up their secrets.
My advice would be to get some Smoky Mtn Blackbird Soft Hackles from Hugh. Someone had a link to his site above, and learn how to use a Softhackle, in addition to Dries and Nymphs (I've had it save many a day that were starting to look fishless). You should also use a dropper/dry technique to double your odds if you are not already doing it.
And remember it IS Summer and the LR is low right now. I was up Tremont the other day and the water is low, slow and warming (66 degrees at 8p on 7.16.0. The fish are just trying to survive in many spots, so you may not find them interested in anything. You might try to fish up somewhere high for Brookies or over in the Little Pigeon drainage, it seems to be doing better.
But most of all, don't give up. Its not just about catching fish. If it was, there are a whole bunch of places you could go to increase your odds of catching...
"Even a fish wouldn't get into trouble if he kept his mouth shut."