With tropical storm-force winds extending outward up to 390km from its centre off the northwest coastal town of Apalachicola late on Monday night, forecasters said Debby menaced a broad swath of inland territory with flash floods.
"Torrential rains and flooding will continue for the next few days across portions of the Florida Panhandle and North Florida," the Miami-based National Hurricane Centre said.
Apart from coastal flooding, from storm surge and wind-whipped rising Gulf tides, it said tornadoes were possible through Tuesday along the Florida Peninsula.
Governor Rick Scott declared a state of emergency earlier on Monday and a tropical storm warning was in effect along much of the Gulf coastline.
"Because of the broad impact of Tropical Storm Debby, virtually every county in Florida could be affected," Scott said in a statement announcing the statewide emergency.
Gas production interrupted
"Some communities are already grappling with flooding, wind damage and electrical outages," said Scott, who ordered all state agencies, including the Florida National Guard, to provide any necessary assistance requested by local governments.
The Hurricane Centre said Debby, the first named storm of 2012 to move into the Gulf of Mexico, was packing top sustained winds of about 72km/h and forecasters predicted little change in strength over the next couple of days.
Over the weekend, the storm idled about a quarter of US offshore oil and natural gas production in the Gulf of Mexico, based on figures issued by US offshore regulators.
But on Monday, after the storm had veered away from the Gulf oil patch, big offshore drillers like BP Plc and Royal Dutch Shell began returning staff to offshore platforms.
Forecast models show Debby making landfall along the northern Florida Gulf Coast later this week.
Dubbed "Debby Downer" in some local media reports, it could dump more than 30cm of rain in some areas of the state, with isolated amounts of more than two feet in north Florida, the hurricane centre said.
Thousands without power
Flash flood warnings were in effect for many areas, including some where streets were already under water, and emergency management officials cautioned that inland flooding was associated with more than half the deaths from tropical cyclones in the United States over the last 30 years.
"Gulf Coast residents and visitors should take Tropical Storm Debby seriously," said Federal Emergency Management Agency director Craig Fugate. "Flooding with Tropical Storm Debby is a very big concern for the Florida Panhandle and portions of the southeast."
Florida officials said the storm had left tens of thousands of people without power and forced the closure of key highways and bridges in the Tampa Bay area, including a 6km span connecting the city of S. Petersburg with the Bradenton area.
On Sunday, Debby spawned twisters that killed a woman, badly injured a child and wrecked homes in central Florida in rural Highlands County, according to an emergency management official.
Florida's Pinellas Country was also hit hard, with flooding in some areas and at least 20 houses with roofs that were partially or fully blown off during a tornado-like storm on Sunday.
In Alabama, rescuers continued a search on Monday for a swimmer who is presumed dead after he went missing off the Gulf Coast near Orange Beach on Sunday.
Though Debby's track was still uncertain, the hurricane centre said it could re-emerge and gain strength over the western Atlantic Ocean by next weekend.