Not yet a hurricane, Tropical Storm Isaac — after killing at least three in Haiti — churned Saturday evening along the north coast of Cuba toward Key West with the likelihood of a glancing blow to Miami-Dade.

With the threat that the storm could hit the Florida Keys as a possible Category 1 hurricane, Florida Gov. Rick Scott issued a state of emergency as the Republican National Convention announced that events in Tampa would be postponed until Tuesday.

In South Florida, local officials announced that schools will close Monday in Monroe, Miami-Dade and Broward counties. In the Lower Keys, which boasts a high transient population, at least 35 people had checked into a hurricane shelter at Key West High School on Saturday evening.

That included Delores Conway, who normally sleeps at a Stock Island homeless shelter. A hurricane brought Conway to Key West — after Wilma in 2005, she arrived looking for post-storm repair work.

The images of that storm were enough to convince her to play it safe at the shelter Saturday night.

“It looks like the safest place at the moment,” Conway said. “People showed me pictures they had taken where their houses were messed up and their cars were gone.”

Up in Miami-Dade, County Mayor Carlos Gimenez on Saturday afternoon issued an evacuation order for people living in mobile homes, unsafe buildings and homes in low-lying, flood-prone areas. The county opened three shelters in South Miami-Dade, and ordered non-essential county staff, about half of the 27,000 workforce, to remain at home Monday.

By 5 p.m. Saturday, according to the National Hurricane Center, the storm — with winds of about 60 miles per hour — had strengthened little as it hugged the north coast of Cuba. But Isaac’s core is slated to be near hurricane strength by early afternoon Sunday as the system chugs near Key West.

The Florida Keys and Southwest Florida remain under a hurricane warning, with Miami-Dade under a hurricane watch. Tropical storm warnings and watches were extended up the east coast to Suwannee River.

The northern coastline of Cuba, on Saturday evening, was feeling the brunt of Isaac’s weather.

Havana’s Meteorological Institute reported that the storm touched down in Maisi, a municipality east of Guantanamo Saturday afternoon.

Radio Baracoa reported that two homes in the island’s eastern most city of 48,000 had collapsed and that the storm surge had thrown up a lot of debris on its seaside Malecon boulevard and nearby streets.

But the storm’s drama fizzled at the U.S. Navy base at Guantánamo Bay, Cuba, where the military had scrapped this month’s Sept. 11 terror trial hearings and evacuated staff and observers from the crude compound called Camp Justice.

“The bad weather did not materialize here as tropical storm Isaac turned away and headed up the East coast of Cuba,” said Navy Capt. Robert Durand, the detention center spokesman.

The base did not report any damage or injuries in what amounted to a splash of summertime rain. Soldiers embarked on late-morning runs around the 45-square-mile base, while the base commander ordered the cafeterias reopened in time for 5:30 p.m. Saturday supper.

Forecasters believe the system’s jaunt over Cuba will be brief — and allow the storm more time to strengthen in the warm waters of the Florida Straits.