I live in a fixed rent apartment complex. My lease is up in 3 days I need one month before my new home is ready, I can not afford to move twice. My apartment complex will not give me a month extension and telling me I need to renew my lease or move out. I have nowhere else to go, should I just stay and have them evict me or sign new lease and break it? I really don't know what to do.

Why would you open yourself up to a law suit; small claims court; both of which will cost you money. Move yourself into a hotel for the short stay; put your furniture in storage. I think that is a better short term option then anything else!