How cold should Evaporator Coil Unit feel?

I have a central heat/air unit and it seems to be working overtime. Its been really hot and humid for the last couple of weeks. The unit runs all the time from noon until after the sun goes down, then kicks on and cools everything down and kicks off like normal. The drain pipe from the evaporator coil stopped up at the evaporator and water dripped out of the bottom of the evaporator and soaked the floor. I changed the filter and the old one was dirty but didn't seem like it was excessive. I got the drain unstopped and there hasn't been another soaking (it still runs all afternoon without kicking off). I've been keeping a close watch and the drain gets cold enough for water to condense on the surface of the fittings at the evaporator and on down the tubing that leads outside. The outside surface of the evaporator feels really cool but there's no water build up. Everything seems to be draining normal again, but the condensation on the drain tube and the coolness of the evaporator has me kinda gun-shy. Does this sound like a one time stopped up drain problem, or something more complecated?

Sounds normal to me. If you had neglected the air filter, you could have a lot of crud on the fins of the evaporator coil. If that is dirty, it reduces the efficiency of the unit, and the accumulated dust is a good place for smells to originate and things to grow. So, it might be worthwhile checking and maybe cleaning that if necessary. You need to do this carefully, since if you bend the fins, you decrease its ability to function well.

Hello, as a rule of thumb, you want to see about a 20 degree difference, or(the split), between (The Return Air) (Air enteriing the Evaporator), and (The Supply Air), (Air Leaving the Evaporator). Some units will procuce a little less, and some a little more. The biggest factors in the split, are a Clean Condenser, a Clean filter, a Clean Evaporator Coil, and the Correct Refrigerant Charge. As far as your unit running without Cycling, it could be one of the above, (which I would check first), or things such as Duct Leakage, poor Insulation,etc. Since I do not know how old your unit is, and if It ever did cycle more frequently, (on a hot day), I will just say that an undersized unit could cause this as well.
Good Luck!

Yes izenglish is correct but also you should make sure evap. coils are clean for maximum air flow