First off, I'm wondering how you can give proper care to 9-12 patients. That's a heavy patient load, and it's also a patient safety issue. What happens if you have a few fall risk patients who need to use the restroom at the same time? You can't leave one to get to the other, but you can't ignore the other because you know damn well they'll hop out of bed and attempt to ambulate to the restroom. I'm in the flex pool at my job (meaning I get floated to whatever unit needs the help that specific day) and the most patients I've had at once is 8. That was in our "observation" unit, where the majority of patients are independent. I can't imagine having 12 patients and half of them being a 1x or 2x assist, if not total care.
Additionally, it sounds to me like your unit doesn't work as a team. There are many shifts that I don't finish up all of my duties. Sometimes things just happen in the last hour and a half that prevent you from tying up loose ends. The other night, we got 3 new admits within the last 2 hours so I was unable to change sheets, clean up my last few patients, and tidy up their rooms. So while giving report to the oncoming techs, I let them know what still needed to be done. Know what we did? For the next 45 minutes, we worked together to get start of shift vitals, linen changes, and baths. That way, the oncoming tech didn't feel like I was leaving them with work to do AND all of the patients (and their rooms) were cleaned, changed, and ready for the rest of the day. And we got it done quickly because we worked together. It's so much easier to bathe and change the linens on bed rest patients when you've got help.
And, yes, some techs are just a-holes anyway. I've noticed that the student nurse techs at my hospital are the ones that are the best to work with. The ones that have been techs for years are the ones that like to make a stink about "not pulling your workload". Instead of reporting you, she should have come to you and said "Hey, don't know if you know or not, but this is what should be done. Would you like me to help you so you can see how to do it efficiently so you're not running around at the end of the shift trying to get everything done?"
Sounds to me like you're on a crappy unit that has no concept of teamwork. We have one of those units at my hospital. Whenever I'm on that unit, I'm made to feel like I'm incompetent and I'm spoken to like I'm an idiot for not doing things their way (keep in mind, I'm part of the Flex Unit- and each unit in my hospital has different standards for what they expect out of the techs each shift). But when I'm in other units, the nurses are usually pretty surprised that I'm willing to do work. I've had nurses tell their charge nurses that they're suprised to see someone who actually does work. On units like critical care where the nurse to patient ratio is pretty low (we have a 2:1 ratio for our level 1 CC pts), some nurses are so used to doing all of the work including bathing, linen changes, lab draws, etc. that they are surprised when I'll step in and offer help. But on another *unmentioned* floor, the nurses couldn't be bothered with doing any other than administering meds and expect the techs to do everything else.