If I just signed lease and the landlord failed to do the work promised, can I get out of the lease?

If the work the landlord promised to do is something minor, that would not be sufficient grounds for getting out of the lease.  A lease is a contract between landlord and tenant.  If there is a minor breach of the contract, that would not be sufficient.  If the work that wasn't done is major, you may be able to get out of the lease as this would be a material breach which goes to the basis of the bargain.  In every lease, there is an implied warranty of habitability which requires the landlord to maintain the premises in a habitable condition by complying with local and state housing codes.  When there is a breach of the implied warranty of habitability, the tenant notifies the landlord and the landlord is required to respond within a reasonable time by making the necessary repairs.  If the landlord fails to respond within a reasonable time, the tenant has the following options:  The tenant can make the repairs and deduct the cost from the rent or the tenant can move out and terminate the obligation to pay rent for the balance of the term of the lease or if the tenant stays on the premises, the tenant can withhold rent and defend against eviction.