Here's what the official FLL airport website says under the Flight Information section of Frequently Asked Questions:
"How early can I check my luggage?
The answer varies by airline so contact your airline for their policy. Typically you can check your luggage anywhere from two to four hours prior to your flight."
FLL is my home airport. I know that TSA lists processing times at some of the checkpoints. In theory, they say don't want you to go through the checkpoint until your listed time. In practice, I've never seen that enforced.
I think the bigger issue is when your airline will accept luggage. Perhaps call/contact the airline and see what they say?