The mother and her baby were killed in New Hanover County when a tree fell on their house, North Carolina Governor Roy Cooper told media late Friday.
"I feel like the dumbest human being who ever walked the face of the earth", Ballance said.
Meteorologist Ryan Maue of weathermodels.com said Florence could dump a staggering 68 trillion litres of rain over a week on North Carolina, South Carolina, Virginia, Georgia, Tennessee, Kentucky and Maryland.
They added that the onslaught would last for hours because Florence was barely creeping along at 9km an hour and still drawing energy from the ocean.
Florence already has set a North Carolina record for rainfall totals, exceeding that of Hurricane Floyd, which struck in 1999 and caused 56 deaths.
Florence made landfall 10 miles east of Wrightsville Beach, North Carolina, on Friday morning as a Category 1 hurricane with 90 mph winds.
Although it has been downgraded to a tropical storm, slow-moving Florence is already blasting North and SC with torrential rain and severe floods.
The NWS says southern and central portions of North Carolina into far northeast SC are expected to report an additional 10 to 15 inches of rainfall - with storm totals between 30 and 40 inches along the coastal areas south of Cape Hatteras.
Morehead City, North Carolina, had received 23 inches (58 centimeters) of rain by Friday night, and forecasters warned Saturday morning that parts of the Carolinas could get up to 15 inches (38 centimeters) more. Along coastal communities, people trapped in homes by relentless flood waters awaited rescue, and tens of thousands hunkered down in shelters after fleeing their homes as the storm approached.
The region is being pounded with rain from the slow-moving storm, causing the risk of catastrophic flooding.
Forecasters warned that drenching rains of up to 3 feet as the 90 miles per hour storm crawls westward across North and SC could trigger epic flooding well inland over the next few days.
As the storm hovered around eight miles north of Myrtle Beach in SC, residents in the city of Conway, a few miles from the storm's eye, anxious that the Waccamaw river which surrounds the city would soon burst its banks.
Southwestern Virginia is also expecting up to 10in (25cm).
The death toll is likely to rise.
"New Bern is just not used to this level of a hurricane", Outlaw said.
Florence is forecast to "drop nearly double" the volume of rain over the state compared to Floyd, tweeted Ryan Maue, meteorologist for weathermodels.com.
North Carolina alone is forecast to get 36 trillion litres, enough to cover the Tar Heel state to a depth of about 25 centimetres.
In New Bern, population 29,000, flooding on the Neuse River left 500 people in peril.
In Jacksonville, North Carolina, next to Camp Lejeune, firefighters and police fought wind and rain as they went door to door to pull more than 60 people out as the Triangle Motor Inn began to crumble.
"WE ARE COMING TO GET YOU", the city tweeted around 2am.
Boat teams including volunteers rescued some 360 residents, including Sadie Marie Holt, 67, who first tried to row out of her neighbourhood during Florence's assault. Water rescues were also underway, although it was hard to know how many had occurred. But Outlaw said on Friday morning it's "not a bad idea to get in your vehicle and get west of I-95" if residents feel they can safely do so. Officials in South Carolina's Craven County say conditions are much worse than some residents expected, with almost 500 people calling the local emergency services hotline asking for help.
"Honestly, I grew up in Wilmington". Local media said she had suffered a heart attack.
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