I had one of those jobs for two+ years (just ended recently). It was awful, but it paid well. I did learn some stuff, so that was good. But I was overqualified and generally unhappy with the work.
Sometimes you have to suck it up in silence and just struggle through. I'm not saying this to disparage your position: this is what I told myself every day for those two+ years. I liked almost everyone I worked with a lot, and that helped. It's just that the work was dull and I often wanted to quit. But I couldn't. I saved money and as a result am now not in the same situation I was in when I started, so that's good too.
Now I've lost my job and I'm looking for something else.
My best advice is to keep your head down at work and just do what the employer wants. The longer you follow this path, the more likely you'll be to get a raise or promotion.
It sucks. I know. But you have to do the best you can, and if you need the money to pay the bills, you may as well accept that you have to take something you don't like now, in the hopes that you'll find something better later.
Some ideas:
* Is a local governmental representative hiring (state or federal senator, member of the house, etc.)? These jobs pay okay-ish and the work can be extremely rewarding. I did social security casework after I graduated (helped constituents who got lost in the system on behalf of the member of Congress) and received grateful phone calls from people I'd helped all the time (weekly). I also learned a lot about the government. This has a way of letting you see that the work you do is worthwhile and meaningful.
* What about other non-profits? Even entry-level stuff can be meaningful, and promotions are always possible.
Send me a PM with a bit of info on your background if you like, and maybe I can come up with some more ideas.