Look at your lease to see what it says, if anything, about the amount of notice you are entitled to receive in the event of a rent default. If nothing is there, then it would be provided by statute which you'll need to find out as I don't now Texas law. (Here, in California, the Landlord is required to give the tenant a notice to pay rent or quit so the tenant can fix the default before the Landlord could try to evict.)
If the Landlord accepted your late payments, then the Landlord also may have waived any right to evict you. If you have a lease that is more than a month to month tenancy, the acceptance of rent would be (at least in California) a waiver of any rent default.
Unless the Landlord resorts to self-help (illegal here in California), he/she can't really force you out in 14 days as, I imagine, it would take longer to get to Court and get a judgment for possession.
I think you need to speak to an attorney if the Landlord is really serious. If you can't patch up the problem and the Landlord insists that you move, you may have no choice but to seek legal advice.
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