This depends on what you agreed to in the lease. If it's a stated lease term (for example, one year), the landlord after receiving your notice of termination has to make reasonable efforts to re-rent the property. You would be responsible for any amounts you agreed to pay for the term for which the landlord does not receive rent from someone else. If it's a month to month lease with no stated term, it can be canceled by either party with one month notice before the next. If you gave proper notice, you would not be responsible for the next month's rent. It's also possible that your state has tenant laws that might protect you in this situation since it's such a short time after signing and you never occupied the home, so you want to check that as well.