I agree with those who are encouraging looking for other employment before turning in your notice.
This.
I'm curious, does the job pay well? If so, then why not use this as an opportunity to gain some emotional intelligence and grit? I used to run a department in an automotive parts manufacturing plant, 21 direct reports on three shifts. It was similar to what you're describing--cutthroat, negative, stressful, etc. There was a daily 7am morning management meeting where people would spend the entire 30 minutes tearing each other down. My girlfriend almost left me because I brought the stress home, I didn't sleep, and it sucked. However, the job paid very well and I didn't have the cash to quit.
I interviewed a couple times, and found that I was most likely going from the frying pan and into the fire by just trying to "get out". I needed goals to work towards, like early retirement or owning real estate to keep me focused. Once I made this realization, I looked at my job as a way to achieve those goals, and not my life. It helped me sleep better, and suddenly all of the negativity and backstabbing rolled right off my back. And the funny thing about bullies like I worked with is that once you stop letting them bother you, they stop trying. I was suddenly a spectator watching stupid people fight among themselves. I ran my department, helped my employees out where I could, and I started applying to jobs that I was interested in. Once I made the switch from "running FROM something" to "running TO something", I was much more successful in my interviews. I ended up with a much better job making $15k/year more.
Every now and then, someone will try to bait me into getting upset about something, but now I can recognize it and let it roll off like water on a duck's back. That's emotional intelligence, and I wouldn't have it if I hadn't worked my crappy job. Use your shitty job as an opportunity to grow, and run TOWARDS a new job, not AWAY from your current job.
Just my 2 cents.