Andrea crawling ashore in Florida's Big Bend

(CNN) -- Tropical Storm Andrea began to crawl ashore in the swampy, sparsely populated Big Bend region of Florida on Thursday afternoon, bringing heavy rain and winds up to 65 mph with it.

At 5 p.m. ET, the National Hurricane Center in Miami reported landfall was imminent.

In Taylor County, Emergency Management Director Dustin Hinkel said landfall was expected about 190 miles north of Tampa, between the towns of Steinhatchee and Horseshoe Beach.

"We've had good luck with the storm coming ashore during low tide, so we have had some very, very minor coastal flooding so far," Hinkel said. "The rain has been very manageable here."

Tornado watches and sporadic warnings covered most of the state's peninsula, and forecasters warned of coastal flooding as the storm neared land.

Andrea, the first named storm of the Atlantic hurricane season, is projected to cross northern Florida and southern Georgia before skirting the Atlantic coast on Friday, bringing heavy rain and the potential for flash floods along the Eastern Seaboard.

But it didn't enough time over the Gulf of Mexico to develop into a hurricane before its projected landfall in the crook of the state's west coast, the Miami-based National Hurricane Center reported.

Taylor County issued only a voluntary evacuation call as the storm neared, aimed at people living in mobile homes and older buildings, Hinkel said. No evacuations were ordered in in Dixie County, to the south, said Tim Alexander, the emergency services director there.

"We're experiencing quite a bit of rain, some tropical storm winds, and anticipating about a 3-foot storm surge," he said.

Andrea's main threat will be torrential rain -- perhaps as much as 6 inches.

"We will have some low-lying freshwater flooding," Alexander said. "We don't anticipate, if it holds, that we'll have anybody stranded or have to evacuate anybody."

And many Floridians sounded unimpressed as Andrea neared land.

Though it's set to soak Tallahassee, Sue Carpenter doesn't expect Andrea to deter many of her dedicated students at Lifelong Fitness Pilates. By 8 a.m., none of her private class clients had called to cancel.

"They're dedicated," Carpenter said.

Across town at Mike's Liquor and Beer Barn, the delivery trucks arrived earlier than usual Wednesday morning.

"We'll see an upswing" in business during the morning, owner Mike Raynor said. "But I think it's not gonna be anything special, nothing real bad. It's been so long since Tallahassee had a storm. Today, I think people are just now realizing it's coming."

At 5 p.m. Andrea was about 35 miles north-northwest of Cedar Key, Florida, and had picked up speed as it chugged toward shore. It was moving to the northeast at 17 mph, the Hurricane Center reported.

The storm triggered tornado warnings around Tampa on Thursday morning, while tornado watches were posted for much of south Florida as bands of rain fell there. Forecasters warned that could cause "minor to moderate" flooding during high tides and minor flooding in urban areas.

"We are already getting the outer bands here in Tampa Bay," CNN commenter Angel MacFarland Armstrong wrote. "Lots of rain, flooding, and there have been several confirmed tornadoes overnight and this morning."

Radar indications pointed to tornadoes east and south of Tampa, and meteorologists detected one twister near the community of Myakka City, about 25 miles inland from Sarasota.

Tropical storm warnings stretched from Boca Grande, near Fort Myers, to the mouth of the Ochlockonee River, south of Tallahassee. On the East Coast, warnings were also posted from Flagler Beach, Florida, about 70 miles south of Jacksonville, to the southern reaches of Chesapeake Bay.

The area in the bull's-eye is roughly where Tropical Storm Debby hit nearly a year ago, in June 2012. Debby dumped up to 2 feet of rain onto the low-lying region, causing extensive flooding in some coastal towns.

Andrea is expected to cross southeastern Georgia, bringing as much as 8 inches of rain in some areas, and continue into the Carolinas. The eastern parts of North and South Carolina could see up to 4 inches of rain, the National Hurricane Center said.

"The combination of a storm surge and the tide will cause normally dry areas near the coast to be flooded by rising waters," according to the center.