Toaster wire heat is the norm here in south Florida but our heating season is measured in days and usually not even all day then. My wife turns it on in the morning while she is getting ready to go to work and turns it off when she leaves.
A heat pump would not do much in that short amount of time.
A heat pump is nothing more than an air conditioning unit with a reversing valve. It's a negligible cost increase over typical AC systems, and will heat just as fast as the AC cools, and just as fast as a resistance heater of similar size. I'm surprised they'd use anything other than heat pumps in Florida.
At 12 cents/kWh, a 1500W electric resistance heater of the type you can get for $15 at Wal-Mart will cost $129/month to run. An electric heat pump would only cost $43/month. Insulating/sealing the room so you don't have to run it 24/7 would help considerably as well