Will I get fired for telling my squad leader that I am tired of doing his job?

I started working at Dartmouth College a week before my squad leader. My supervisor told me that I should show him how to use the equipment at work. Not a problem. But my squad leader is suppose to carry the radio incase something happens or some one needs to get ahold of us. Well he will not do it. I have to. He's also suppose to do invitory for our department, deligate with other building squad leaders, know wha tto do incase something happens and how to fix any problem that might arise with the equipment. But no. I have to do all of that and more. It's been six weeks now and I'm tired of it. He's making alot more then me to do nothing but complain, cuase trouble. He's already broken three carpet machines. He doesn't listen when I tell him where he's going wrong. So I told him the other night that I was tired of doing his job. He got all defensive. Telling me that I'm not doing his job. And that he's going to report this to our shift supervisor. He can go a head. The supervisor already knows. He's the one that told me to train him. Well it's been over a month. The quad leader should be squad leader now. Not me.