Here in FL, there is no specified time for the landlord to begin repairs from a disaster of this nature. The law says a landlord must make repairs in a reasonable time and what is reasonable is based on the circumstances, including availability of people to do the work and availability of materials and time it takes for insurance to adjust the claim.
If the property is not habitable, you have a right to insist on the landlord either paying for you to live elsewhere until the damage is repaired or reducing the rent based on the time the premises is not habitable, at the landlord's choice, or you can terminate the lease. You cannot tear out anything without permission of the landlord.
If the premises needs extensive repair the landlord can insist you move out until repairs are completed if you have a written lease for a term that has not expired, but again they have to pay for you to stay elsewhere or reduce your rent by the time you cannot use the premises.
With the severity of damage caused by Irma here in FL, there could be a shortage of contractors or materials to make repairs, so as long as the landlord is beginning the process, they are not violating the lease duties regarding repairs and they will be at the mercy of contractors and insurance adjusters.
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