I feel like I'm trapped, and I don't know what to do here. I started working a temp job at the end of May that was advertised as data entry and was supposed to last 2-3 months. It was to help implement a specific project and the job description literally said it was “copy and paste”. Turns out it was much more complicated than that, and my immediate supervisor is the only other person working on it in the company, in addition to her regular job.
At the 3 month mark, I asked if the assignment was ending, and was told the company wanted to hire me on permanently but that a position would need to be created and that “takes time”. They gave me a “hopefully before Labor Day” time frame. It's now late October, the subject of the permanent position seems to have been dropped, and I'm being given work that is WAY above my pay grade and not what I signed on for. I wrote the temp agency an email explaining all this, told them if I'm going to stay on as a temp long-term with more responsibility I'd like to revise my rate of pay to reflect this, and got ignored. I've tried to talk to them multiple times and got the brush-off. My supervisor at the job doesn't want me to leave because then she'll be stuck doing the work, so she won't intervene. I share an office with her – we are literally less than 2 feet away from each other at all times and I can't stand it anymore.
I really want to leave this job, but I need unemployment insurance. They told me 2-3 months at the beginning, I've signed no contracts, and I am totally being taken advantage of here. How do I get out of this and still get unemployment while I find another job?
Edit: I work in New Mexico, the temp agency is in Denver, CO.
TL;DR: Temp job pulled a bait and switch, said job was 2-3 months, now it's going on endlessly. Can I leave and still get unemployment?