SAVANNAH, Ga.—Nervous residents rushed to buy plywood and generators while emergency officials in Georgia, Florida and the Carolinas weighed possible evacuations Tuesday as Tropical Storm Hanna shifted toward a tough-to-predict landfall along the southern Atlantic coast by the end of the week.

Florida Gov. Charlie Crist declared a state of emergency as Hannah, downgraded from hurricane status Tuesday but with ample time to regain strength, began a turn to the northwest from the Bahamas. Emergency officials in Georgia and South Carolina went into 24-hour alert mode.

In Savannah, which hasn’t seen a direct hit from a major hurricane in more than a century, Janey Miley took her 15-year-old daughter to Home Depot at lunchtime Tuesday for an impromptu lesson in hurricane preparedness.