Resignation without notice at all - this can include walking off the job, job abandonment, and failure to return to work after a period of leave. No advance notice of termination or resignation is required.In Texas we are under no obligation to accept the two week notice and it is still considered a resignation because they demonstrated intent to leave. You want to give at least a two weeks' notice. Resignation Notice In Texas, employees can resign without giving any advance notice. Accepting a resignation early without paying the employee for the notice period can have consequences, if the employee gave more than two weeks' notice. If he gives two weeks' notice or less, and you accept the notice early within the two weeks, it still will be a "quit," not a discharge. The employer is required to accept your resignation, but doesn't have to accept the offer of 2-weeks. When there is an advanced notice of resignation, i.e. Under the Texas Education Code, contract employees are required to resign no later than 45 days before the first day of instruction for the school year.