It had been projected to shift north after making landfall.
"If you don't have a plan in place, you still have time to do something", Jones said.
Town manager Michael Cramer told the New York Times he was anxious Florence would be even more devastating than Hurricane Hazel, which lashed the town in 1954, destroying 362 buildings.
Hurricane Florence in the Atlantic Ocean as it threatens the US East Coast. Current forecasts call for Florence to be at least a Category 3 storm when it arrives at the Carolinas.More news: Apple's greatest magic trick: A $749 iPhone is now "cheap"
A state of emergency has been declared in Maryland, North Carolina, South Carolina, Virginia and Washington amid concern over potential torrential rain and flooding.
Hurricane Florence, heading for the Carolinas, "will likely be the storm of a lifetime" for areas of the coast, according to the National Weather Service early Wednesday.
Thousands of residents in North and SC have fled their homes as Hurricane Florence, the biggest of the extreme weather conditions on the map, looks set to tear its way through the eastern seaboard.
President Donald Trump, warning residents to get out of the way, said the federal government was "ready for the big one that is coming".
Hurricane Florence is expected to make landfall on the eastern seaboard Friday morning, which means Coweta County and the surrounding area could begin feeling the effects of the storm late Friday night and Saturday.More news: Windows 10 warns users not to install Chrome and Firefox
With the storm churning across the Atlantic with 140 miles per hour winds, hurricane watches and warnings include the homes of more than 5.4 million people on the East Coast.
At 11:00 pm (0300 GMT), the eye of the storm was 280 miles (450 km) southeast of Wilmington, North Carolina, moving northwest at 17 mph.
The intensity of the wind and rain we'll see here is dependent on the exact track of the storm.
In Virginia, 245,000 coastal residents were ordered to evacuate.
Forecasters say Florence is expected to blow ashore late Thursday or early Friday, then slow down and dump 1 to 2½ feet of rain that could cause flooding well inland and wreak environmental havoc by washing over industrial waste sites and hog farms.More news: Primary Day: What you need to know
Hurricane Isaac is now moving through the western tropical Atlantic Ocean but will likely bring heavy rain and damaging winds to parts of the Lesser Antilles later this week.