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Tropical Storm Elsa entered the Florida Straits Tuesday morning and is headed towards the Florida Keys after drenching Cuba and killing at least three people in the Caribbean. 

The National Weather Service took to Twitter for a 5 a.m. E.T. public advisory, alerting that parts of Florida are under a hurricane watch, including a portion of the west-central coast and the Big Bend coast. An earlier alert said conditions are "beginning to deteriorate" across the Keys. S

South Florida has already been impacted by the storm, and work conditions have worsened at the building collapse site in Surfside. 

WSVN reported that the storm’s maximum sustained winds hit about 60 mph late Monday and was headed north-northwest at about 12 mph. The storm has been blamed for flooding rains in Cuba and damaged hundreds of homes in Barbados, the BBC reported. The report said the storm now seems to be drifting to the west and will spare Florida from a direct hit.

"The wind is blowing hard and there is a lot of rain. Some water is getting under the door of my house. In the yard the level is high, but it did not get into the house," Lázaro Ramón Sosa, a craftsman and photographer who lives in the Cuban town of Cienega de Zapata, told The Associated Press by telephone.

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The U.S. National Hurricane Center said the storm was expected to be near the Florida Keys early Tuesday and would then pass near or over portions of Florida’s west coast by late Tuesday and into Wednesday.

The Associated Press contributed to this report