When a Notice to Quit is served on a tenant, ordering the tenant to vacate the premises by a certain date, it is actually assumed by the court system that the tenant will not vacate by that date.  If the tenant remains in the premises past the "quit date," that does not give the landlord the right to physically throw him out; to change the locks; to remove his possessions; or anything of that nature.  The tenant's failure to vacate the premises gives the landlord the right to bring a legal action against the tenant seeking a court order for his eviction.  Various detailed procedures must be followed in suing a tenant for eviction, the landlord bears the burden of proving that the tenant is in default of his obligations under the lease (or other rental arrangement, whether in writing or oral) and the tenant has a right to appear in court and raise defenses, both procedural and with respect to the substance of the landlord's claims of default.  It would be advisable to consult with a qualified attorney regarding whether there are defenses to an eviction action that your landlord might file; and how best to protect your rights as a tenant.  If the landlord sues you for eviction, it can take a couple of months before the court makes a final ruling.  If the judge rules against you, depending on the circumstances, the Judge will still give you some additional number of days to vacate the premises before a marshall can be called in to remove you and your possessions.  Thus, this process can go on for several months.  In some cases, before reaching the end of the case, a tenant may be able to pay back rent and make a deal with the landlord that enables the tenant to continue in the premises by agreement.  Even if that is not possible in your case, at least you will have some leeway as to when you will move out.