KEY WEST, Fla.—Two years since a hurricane last lashed at Florida, many residents were taking a wait-and-see attitude Monday as a strengthening Tropical Storm Fay swept across the Florida Keys and bore down on the Gulf Coast.

While tourists caught the last flight out of town and headed out of the storm’s path, residents in the carefree Florida Keys put up hurricane shutters and checked generators, but weren’t doing much more.

“We’re not worried about it. We’ve seen this movie before,” said 58-year-old Willie Dykes, who lives on a sailboat in Key West and was buying food, water and whiskey.

By midafternoon, heavy rains moving ahead of Fay’s core were pelting the low-lying Keys island chain. Sustained winds of about 33 mph bent palm trees, and some gusts hit 51 mph.

The sixth named storm in the Atlantic hurricane season was expected to become a hurricane before curling up the state’s western coast and hitting Florida’s mainland sometime today.

“There are bad storms and there are nice ones, and this is a nice one,” said Becky Weldon, a 43-year-old guest house manager in Key West. “It cleans out all the trees, it gives people a little work to do and it gets the tourists out of here for a few days.”

Officials were worried that complacency could cost lives, repeatedly urging people to take Fay seriously. The message got through to tourists—Monroe County Mayor Mario Di Gennaro estimated 25,000 fled the Keys. Some residents have taken steps since the busy 2004-05 storm years, when eight hurricanes hammered Florida, such as buying generators and strengthening homes, but not everyone is so prepared.

“This is not the type of storm that’s going to rip off a lot of roofs or cause the type of damage we normally see in a large hurricane,” said Craig Fugate, the state’s emergency management chief.

However, Fugate said: “I’ve seen as many people die when I have a blob-shaped asymmetrical storm that they dismiss as not being very dangerous.”

The state took every step to be ready. National Guard troops were at the ready and more were waiting in reserve, and 20 truckloads of tarps, 200 truckloads of water and 52 truckloads of food had arrived.

Fay was blamed for at least 14 deaths in Haiti and the Dominican Republic, including two babies who were found in a river after a bus crash.