Can I escape from a lease term that has not yet begun?

I found out today That I am being terminated from my job. The final day of this month ( March 31st) represents the final day of my one year lease. I did recently sign a new one year lease that is due to begin on the first of April. I have not paid for the first month of the new contract. Contract law states that a contract is an offer, acceptance and mutual consideration. Since I have not paid in part or whole the new lease term is this grounds to nullify the lease based on their not being consideration? I live in Arizona.