How long should I give a landlord to resolve my lack of heat and hot water?

Although the law in your state may be specific, I do not know if there is any real general rule for this.  Your inconvenience for just one day is enough to make you mad in my book.  So I would do this: go down to landlord tenant court and ask to start a proceeding against the landlord for the lack of hear and hot water.  Ask to pay your rent in to court and for an abatement (reduction in rent).  In New York it is called an HP proceeding.  This will insure it is fixed or you are given the option to leave.  You can not just break the lease.  Good luck.