While two weeks is the norm, there are circumstances under which it need not be followed.
I've worked in a toxic work environment in the past. I don't think any less of the people that I watched quit on short notice after continued mistreatment from management; in fact I respected them for not putting up with any more crap when the didn't need to. Assuming this environment is as toxic as described by OP, it's important to remember that many of your coworkers around you will empathize with your decision and respect you standing up to the manager that they too resent.
I've worked in a toxic work environment in the past. I don't think any less of the people that I watched quit on short notice after continued mistreatment from management; in fact I respected them for not putting up with any more crap when the didn't need to. Assuming this environment is as toxic as described by OP, it's important to remember that many of your coworkers around you will empathize with your decision and respect you standing up to the manager that they too resent.