CBS NEWS - With the July Fourth weekend on the horizon, the Atlantic hurricane season's first named storm was slowly strengthening off Florida's coast early Wednesday, though Tropical Storm Arthur wasn't yet spooking too many in the storm's potential path.
"I think everybody's keeping one eye on the weather and one eye on the events this weekend," said Joe Marinelli, president of Visit Savannah, the Georgia city's tourism bureau.
As of 2 a.m. EDT Wednesday, a tropical storm watch was in effect for a swath of Florida's east coast, from Fort Pierce to Flagler Beach.
The National Hurricane Center urged those as far north as parts of Virginia to monitor Arthur's path.
The center said Arthur was becoming better organized and predicted it would become a hurricane by Thursday.
Early Wednesday, forecasters said the storm was meandering about 95 miles off the coast of Cape Canaveral, moving north at about 5 mph, with maximum sustained winds about 60 mph.
Forecasters said Arthur is likely to stay just offshore, passing northeastern Florida Wednesday night and moving parallel to the southeastern U.S. coast on Thursday.
Off Florida's Space Coast beaches - the closest to Arthur - the sky was cloudy and winds fairly normal Tuesday, said Eisen Witcher, assistant chief of Brevard County Ocean Rescue.
Red flags warned of rough surf, and beachgoers were advised to get into the water only in areas with staffed lifeguard stands. But overall, Witcher said, it was "business as usual."
Red flags also flew at Daytona Beach. By mid-day, a dozen swimmers had been aided by lifeguards when they got caught in a rip current. On any given day, 15 to 20 swimmers need help, said Tammy Marris, spokeswoman for the Volusia County Beach Patrol.
Near the storm, 19 ill crew members were evacuated from a South Korean cargo ship after they showed signs of food poisoning. The JS Comet was anchored three miles off Cape Canaveral, and the Coast Guard reported that deteriorating weather conditions were one factor in the decision to evacuate.
Hurricane watches have been issued for the Carolina coast.
Forecasters are also warning people about upcoming rain, heavy surf and swells, and rip tides.
In North Carolina's Outer Banks, officials said they would close Cape Lookout National Seashore at 5 p.m. Wednesday and reopen when it's safe.
The motel Shutters on the Banks was completely booked for the holiday weekend, general manager John Zeller said, despite forecasts for potentially heavy rain, gusty winds and isolated tornadoes late Thursday and Friday.
"We have received some cancellations but not too many," he said. "Basically we are telling people to kind of wait and see what happens."
The motel has a 72-hour advance notice on cancellations, but Zeller said it will be waived if the storm tracks toward the area or warnings are issued.
In Folly Beach, South Carolina, dozens of people fished from the pier under sunny skies Tuesday. Others surfed on gentle swells, sunbathed and looked for shells.
In Savannah, rooms in the downtown historic district were expected to be at least 80 percent full for the holiday weekend, when crowds pack the beach on neighboring Tybee Island.
Cancellations aren't uncommon when storms approach, but those calls weren't coming in Tuesday, Marinelli said.
Amy Gaster said her Tybee Island vacation rental company had more than 200 beach homes and condos booked for the weekend, likely to be the busiest of the year. If forecasts start to show a serious threat, Gaster said her staff is prepared to send alerts to guests' cell phones.
But as long as Arthur stays offshore, she said her biggest concerns are rip currents and possible thundershowers on Thursday, when thousands are expected to pack the Georgia coast's largest public beach for fireworks.
"Hopefully Mother Nature is going to cooperate with us this year," Gaster said.