"I think we're going to all enjoy a nice summer day," said Sally Bishop, the county's emergency management director.
Flooding is still a concern as Fay moves up the peninsula, with up to 25cm (10in) of rain forecast. A storm surge of up to 1.5m (5ft) above normal is still possible and the storm could also trigger tornadoes.
Heavy rain was also drenching Cuba, which suffered some flooding but no major damage.
Fay's passage over Haiti and the Dominican Republic was more destructive, with more than a dozen deaths reported.
There was confusion over an accident in Haiti, where a truck carrying up to 80 passengers plunged into a swollen river on Sunday.
Officials and witnesses said more than half the passengers were missing, with many feared drowned.
However, UN peacekeepers stationed in Haiti who arrived at the scene told the Associated Press that two babies had died in the accident but that 41 passengers had escaped to safety.
A civil protection officer, who had earlier said some 30 people were feared dead, also told AP that three bodies had been found.
Fay is the sixth tropical storm of the 2008 Atlantic hurricane season.
Two of the tropical storms so far, Bertha and Dolly, have reached hurricane strength.
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