Debby, now strengthening rapidly in an unusually warm Gulf of Mexico, is expected to become a hurricane Sunday night and slam into Florida's Big Bend region around mid-day Monday.
The National Hurricane Center warned there is a danger of life-threatening storm surge along Florida's Gulf Coast with six to 10 feet (1.8 to 3.0 meters) of inundation above ground level in some areas.
The storm will probably cause catastrophic flooding with "potentially historic heavy rainfall" when Debby moves northeast across Georgia and South Carolina over the next few days, the NHC said.
"We are looking at potentially really, really significant flooding that will happen, particularly in north-central Florida," state Governor Ron DeSantis told an emergency briefing on the storm Sunday.
He and NHC deputy director Jamie Rhome have stressed that Floridians should be making and completing their final preparations immediately.
As of 5:00 pm (2100 GMT), Debby was about 120 miles (190 kilometers) west of Tampa, carrying maximum sustained winds of 65 miles per hour and moving north at 12 miles per hour, the advisory said.
As residents rushed to prepare, mandatory evacuations were ordered late Saturday for part of Citrus County, Florida, with eight other counties under voluntary evacuation orders, local media reported.
"Take the situation seriously," Paul Hasenmeier, Hernando County fire chief and public safety director, told reporters late Saturday. "We know the water's going to come up as the storm passes."
Debby is expected to dump six to 12 inches of rain in parts of Florida, and as much as 20 to 30 inches in coastal Georgia and South Carolina before the week is over, the NHC said.
The governors of Georgia and South Carolina have declared a state of emergency ahead of the storm's arrival.
Brennan predicted "multiple days of very, very heavy rainfall" -- at possibly record-breaking levels. He said there likely will be severe flash flooding "in areas that don't normally flood."
President Joe Biden on Sunday approved an emergency declaration for Florida, allowing federal aid to be expedited.
DeSantis has activated the state's National Guard, with 3,000 service members on standby to help with storm response.
