Heavy rainfall is expected from western Cuba to Florida an through the northeast Gulf Coast through the weekend.
Forecasters believe at some point later in the weekend, Alberto will reach tropical storm status.
In its 4 p.m. advisory, the National Hurricane Center said the storm had changed little in intensity, but was slowly drifting east. It still remains an unorganized mess as it meanders off Mexico's Yucatán Peninsula but is expected to churn northward into the Gulf of Mexico and approach Florida this weekend.
Only eight Atlantic named storms have formed in the last week of May since 1950, according to Phil Klotzbach, a research scientist in the Department of Atmospheric Science at Colorado State University.
Forecasters say chances are increasing for the first tropical weather system of the year in the Gulf of Mexico.
An Air Force Reserve reconnaissance aircraft is scheduled to investigate the low this afternoon.More news: Harvey Weinstein couldn't fit into regular-sized cuffs
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More news: Alberto stationary, expected to move north and strengthen
Even though South Florida is not in the projected path of Alberto, the region is on the east side - the wettest side - of the storm.
This incarnation of Alberto had the decency to wait and form after the official start of the hurricane season, but then wasted that goodwill by making landfall in Florida.
The large band of low pressure lurking over the Yucatan Peninsula, off the coast of eastern Mexico, is threatening Florida and other southeastern states with heavy rain and flash flooding. The latest rainfall predictions from the National Weather Service's Storm Prediction Center call for 1-3 inches of rain through next week in south Louisiana.
Flood watches already have been issued from Alabama to Georgia.
The National Hurricane Center predicts that Alberto could have sustained winds of 65 miles per hour - not far from hurricane-force - by Monday when it is approaching the coast near Mobile, Ala., and Biloxi, Miss.
The Memorial Day weekend in Texas, however, should be mostly hot and dry. "The main impact will be heavy rains that could exacerbate rivers and areas prone to flooding".