For starters, for all those people who replied and said they manage 20+ patients normally, I think they're blowing smoke. That is by far not the norm. Please don't think it is.
In my most overworked, dumped on days as a tech, the most pts I ever had was 16 and that was ridiculus. Where I work now 6-8 is the norm, even on night shift. In the rare instance that all but one tech calls off and the tech has a floor of 24 pts to themselves, the rules change. The tech does the call lights and the nurses do their own vitals, blood draws, etc and help out wherever else needed.
It's all about team work. I'm sorry they dumped on you so badly. You're house pool or per diem? I'd let the pool coordinator know how badly you were treated. And I wouldn't go back to that floor either. You're right, no body needs that.