Can I break my lease due to a mouse infestation

I recently moved into an apartment in Hudson County, New Jersey. I’ve lived here exactly a month as of this week. I have had numerous problems since the moment I walked in. The worst however started this week, when I noticed out of the blue that I had a severe mouse problem. I’ve seen a total of at least 6 mice. That is only the ones I have seen. Previous to this, I had no evidence at all of such. I have seen cockroaches but thankfully traps have helped take care of that problem. I have notified my landlord and refuses to correct the problem saying that I have to wait for the monthly extermination service which is at the beginning of March. I’ve already seen the mice on my dishes, in towels that I have folded on a shelf in my closet and in places like my kitchen and living room. I am more than disgusted as this to me is a completely unlivable environment. I have not been able to sleep this week which is affecting my work. Do I have the right to break my lease over such a mouse issue? 

Many thanks