Once the date for payment has passed, if you have not paid your rent for that month (assuming you pay monthly), then legally you are in default of the terms of your tenancy. This is true whether you have a written or oral lease. At that point your landlord may file an eviction lawsuit (i.e. an "unlawful detainer"). However, the due date is also subject to any grace period as listed in your lease. For example, some leases provide for 3 or 5 days as such a period. After that, if you have not still paid the rent that you owe, your landlord can sue for eviction.
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