I lost my job in May, and have not been able to find a new one yet. Unfortunately any money I had saved has been spent, and I can no longer pay my lease. I was wondering if there is a way I can break my lease without incurring the penalties that usually accompany breaking a lease.

Probably not, but you'd be better off posting this is the Real Estate forum elsewhere on this site. Unless a responder here just happens to know.

The best thing to do is call your landlord and explain, the sooner the better. Tell him that you're more than willing to have him show the apartment to potential renters, and cooperate in any way you can. He just might let you out of the lease if he can rent it soon.