The sprawling storm was creeping northeast at 2 mph, packing maximum sustained winds of 45 mph along the way.
The storm could also generate a lot more tornadoes across Florida on Tuesday, the National Hurricane Center said.
Debby has stalled several instances in the Gulf of Mexico, dumping up to 5 inches of rain per hour on parts of the Florida Panhandle.
A tropical storm warning is in impact for the Gulf coast of Florida from Mexico Beach to Englewood.
Currently deluged by a stubborn cyclone that would not move, northern Florida could get another six to 12 inches of rain over the next two days as Tropical Storm Debby hovers in the northern Gulf of Mexico.
As of late Monday night, Debby was centered about 35 miles south of Apalachicola, Florida, the weather agency mentioned