There is nothing in the statutes governing residential tenancies that answers this question, so the answer will depend on how your lease defines "breaking the lease". You should review your lease to see what it says regarding this fee.
This answer is for informational purposes only. It does not constitute legal advice and does not create an attorney-client relationship. There may be relevant facts not included in the question that could change this answer. For specific advice, please consult with a licensed attorney in your jurisdiction.
The landlord's remedy for the tenant's violating the lease terms is governed by Florida Statutes 83.595. If your written lease agreement had an early termination / liquidated damages clause and you signed that you wanted that option, then the landlord can charge you for the month that you left / vacated the premises and up to two months' worth of rent in addition to that, no more. If you did not have and agree to an early termination / liquidated damages clause, then the landlord can choose from the three options open to him in 83.595.
Non-payment was the breaching of the lease. Loss of employment is not a defense, so by not paying, you violated the lease terms.
Assuming no early termination/liquidated damages, the landlord can: (1) go after you for the remainder of the lease, (2) let you off the hook from the moment you turned over the keys/from the moment the sheriff let him have possession again, or (3) try to re-rent and give you credit for any rent he can collect from a new tenant.
If you think the landlord is asking for more than the lease or Florida law allows, please see a local landlord / tenant lawyer who can analyze your written lease and the facts and give you an opinion, perhaps even represent you if that is what you wish.