Jeffrey Bush, 36, is presumed dead after rescue crews failed to make contact with him.
Officials in the town near Tampa have postponed further rescue efforts until they determine how much of the ground under the house is compromised.
Sinkholes are common in certain parts of Florida, Hillsborough County's fire chief said.
"Florida essentially sits on a system of caverns," Chief Ron Rogers said, saying water erosion in the caverns causes them to collapse and sinkholes to form on the surface.
The sinkhole is currently 30ft wide and 20ft deep, but officials have established a 100ft-wide safety zone, fearing the top of the sinkhole is growing.