If you're on the small gear on the back, and you have slack in the cable, you won't notice any difference. There should be a bit of tension on the cable even with the shifter all the way in the high-gear position and the RD on the small cog. Have you tried the adjustment with the RD in a middle gear? You should notice a difference within one turn or less. For fine-tuning, I usually go a quarter-turn at a time. What do you mean by the barrel adjuster "near the horns" - is that the one on the downtube cable stops? If so, have you tried the adjuster directly on the RD? Also, is the cable jamming in the housing? Sometimes if the wrong cable ferrule is used (e.g., one for the brake housing), some of the metal strands in the shift housing can work their way out of the housing and stick through the ferrule, adding friction to the cable.