Tropical Storm Ernesto was forecast Tuesday to strengthen before striking South Florida, where residents scurried to make last-minute preparations and lines formed for necessities ranging from gasoline to prescription drugs.

Forecasters at the National Hurricane Center in Miami said the storm, with 45 mph sustained winds and higher gusts, was likely to grow more powerful as it crossed the warm Florida Straits between Cuba and the peninsula. It could reach hurricane strength before it makes landfall as early as Tuesday night.

Forecasters put the chance of tropical storm-force winds hitting Florida at about 70 percent. The number was only 5 percent for hurricane-force sustained winds of at least 74 mph, but forecasters warned Floridians to pay attention even if it doesn’t become a hurricane.

“A strong tropical storm is certainly capable of producing wind gusts to hurricane force and those winds can cause power lines to go down” and can cause roof damage in homes that are already weakened from previous storms, senior hurricane specialist Richard Knabb said.

A tropical storm warning and hurricane watch remained in effect for most of southern Florida, with Ernesto’s rain expected to begin falling by Tuesday afternoon. Ahead of that, people like Migdalia Antigua, 71, were busy getting supplies in case of power outages or other storm-related problems.

Antigua was the first person in line early Tuesday at a Miami pharmacy, buying cholesterol medication and other supplies for her family. Lines were forming across the region at gas stations and groceries and home-supply stores were busy as soon as they opened.

“It’s such an inconvenience,” Antigua said. “But I have my little car and I can move around. All of the responsibility falls on me because I’m the one in the household with my legs under me.”

At 8 a.m. EDT, Ernesto was centered off Cuba in warm open water, about 200 miles southeast of Key West and 215 miles south-southeast of Miami. It was moving west-northwest near 14 mph and could dump 5 to 15 inches of rain.

In Key West, streets were relatively quiet early in the day as rain began to fall. Residents walked their dogs along a coastal road. Some hotels had plywood up over windows, but many homes were unprotected.

Broward and Miami-Dade counties urged residents in mobile and damaged homes to evacuate early Tuesday. “If your home currently has a blue tarp, it is not safe,” Miami-Dade Mayor Carlos Alvarez said.

Gov. Jeb Bush, who has issued a state of emergency for all Florida, warned residents Monday in Tallahassee to have the supplies for the 72 hours after the storm because a “hurricane’s a hurricane, and it has a devastation we’ve already seen. All you have to do is rewind to last year and see.”

With memories of Katrina and the seven hurricanes that have hit Florida since 2004 still fresh, state officials urged residents not to wait before stocking up on supplies and making other emergency preparations.

“This storm should not result in loss of life if people will just heed the safety messages,” said state Emergency Management Director Craig Fugate.

Hundreds of miles of the state’s densely populated Atlantic coast and the Keys were under a tropical storm warning and hurricane watch in Ernesto’s path. A tropical storm warning was extended from New Smyrna Beach on Florida’s Atlantic side and up to Bonita Beach on the Gulf Coast; a hurricane watch remained in effect along the same stretch of coastline.

A tropical storm watch continued on the west coast south of Englewood. Forecasters said a hurricane warning may be posted for portions of South Florida and the Keys later Tuesday.

Over the weekend, Ernesto, the fifth named storm of the hurricane season, became the first hurricane of the Atlantic season and lashed the Dominican Republic and Haiti, killing one woman on a Haitian island.

There were no reports of damage or injury Monday in Cuba, which Ernesto drenched before aiming north toward the warm waters of the Florida Straits.

The Bahamas on Monday ordered boats in southern islands to stay in port. The island chain had a tropical storm warning and a hurricane watch in effect for western islands close to Florida’s coast.

In the Keys, mobile home residents were urged to evacuate and plans were enacted to evacuate special-needs residents to Miami. Miami-Dade County also opened a shelter for residents from the Keys.

NASA scrubbed a Tuesday space shuttle launch and prepared to move Atlantis into its giant shelter at Cape Canaveral if the storm continued to threaten. Cruise ship companies said they were diverting several liners to avoid the storm.

On the Net:

National Hurricane Center: http://www.nhc.noaa.gov