Following a link from +Jeremy Hodges I found this.
According to the federal Uniform Time Act of 1966, states may exempt themselves from observing daylight saving time, as Hawaii and most of Arizona do. But there isn't an option for states to exempt themselves from standard time.
So the change Florida lawmakers desire is technically a change of time zone. The majority of Florida would move from Eastern time to Atlantic time: the zone that's home to Puerto Rico, the U.S. Virgin Islands and the Canadian Maritime provinces. The western part of the state's panhandle is on Central time; residents there would shift to Eastern time.
This weekend, most people in the U.S. will reset their clocks and spring forward. In Florida, there’s a push to never fall back.