With fresh memories of last year's barrage of deadly hurricanes, Floridians kept a watchful eye on Hurricane Dennis (search) on Wednesday as it moved through the Caribbean on a path that could bring the storm to U.S. shores by the weekend.

Forecasters at the National Hurricane Center in Miami cannot say with any certainty where or if Dennis may hit because the storm is still more than 800 miles southeast of Miami. But they cautioned people to be ready for Dennis, which could be a Category 3 hurricane (search) with winds of 111 mph to 130 mph by the time it enters the Gulf of Mexico.

"Pretty much everyone from the (Florida) Keys all the way to Texas" should be monitoring Dennis' progress, the fourth named storm in the young season, said Chris Hennon, a meteorologist at the center.

This is "the earliest we've had this many named storms in recorded history in the Atlantic," said forecaster Chris Lauer.

The Gulf Coast spent Wednesday cleaning up from another tropical storm — Cindy — which left more than 250,000 people without electricity at one point. The storm pelted Louisiana with nearly 8 inches of rain and 70 mph winds, and caused flooding along the coast, including 34 road closures in one Mississippi county. The storm ripped up piers in Alabama, where some area received more than 10 inches of rain.

More than 12 percent of the Gulf of Mexico's daily oil production was shut off Wednesday because of rig evacuations forced by Cindy, a government agency reported. Oil prices climbed nearly 3 percent to finish at a record above $61 a barrel on Wednesday, but the refinery snags caused by Cindy were minor and temporary.

Many New Orleans residents were caught off guard by the strength of the storm.

"When you see oak trees that have been up for 200, 250 years, toppling with the roots intact, that is a pretty impressive sight for a tropical storm," said Capt. Mike Sanders of the St. Bernard Parish Sheriff's Office.

The hurricane season's peak is still more than a month away, but Florida has already been affected by two tropical storms this year. They both brought rain and minor problems to the Florida Panhandle, an area devastated by Hurricane Ivan last year. Florida got pummeled by four hurricanes last year.

"We have all our shutters all prepared," said Jacque Sands, a manager at the Ernest Hemingway Home & Museum (search) in the historic part of Key West.

At 8 p.m. EDT, Dennis' center was about 280 miles east-southeast of Kingston, Jamaica, and about 295 miles south-southeast of Guantanamo Bay, Cuba, forecasters said. A hurricane hunter aircraft found the storm had top sustained winds of near 80 mph; tropical storms become hurricanes when their sustained winds hit 74 mph. Dennis was moving west-northwest at about 13 mph.

Home Depot stores in Florida were not experiencing any rushes for the typical hurricane supplies of plywood, generators and gas cans, company spokesman Don Harrison said. But that could easily change.

"Business is going to pick up as people start watching Dennis," Harrison said.