Forecasters say Dolly was expected to dump 15 to 20 inches of rain and bring coastal storm surge flooding of 4 to 6 feet above normal high tide levels.
Hurricane warnings were in effect from Brownsville north to Corpus Christi, and in Mexico, from Rio San Fernando north to the U.S. border. Tropical storm warnings were issued for surrounding areas and the governor has declared 14 counties disaster areas, allowing state resources to be used to send equipment and emergency workers needed to the areas in the storm's path.
Forecasters said Dolly was expected to make land late Tuesday or early Wednesday as a hurricane with sustained winds of 74 to 95 mph. The storm combined with levees that have deteriorated in the 41 years since Beulah swept up the Rio Grande pose a major flooding threat to low-lying counties along the border. Beulah spawned more than 100 tornadoes across Texas and dumped 36 inches of rain in some parts of South Texas, killing 58 people and causing more than $1 billion damage.
"We could have a triple-decker problem here," Cavazos told a meeting of more than 100 county and local officials Tuesday. "We believe that those (levees) will be breached if it continues on the same track. So please stay away from those levees."
Much of the damage to New Orleans from Hurricane Katrina was from levee breaks instead of wind. Levee breaches in the Midwest made river flooding far more damaging than it would have been earlier this summer.
People in the warning areas have little time left to complete their preparations, National Hurricane Center spokesman Dennis Feltgen said.
"They need to get that done like now. Weather conditions will be deteriorating rapidly later this (Tuesday) afternoon and tonight," he said.
Lines grew at centers giving out sandbags in the Rio Grande Valley. In Brownsville, a utility began draining its resacas -- ponds and lakes formed by old bends in the Rio Grande -- last week to prepare for rain.
In neighboring inland Hidalgo County, officials put out a call for volunteers to man five shelters that it planned to open for residents fleeing coastal counties.
Those who planned to ride out the storm shopped for supplies at a Wal-Mart in Edinburg, 15 miles from the Mexican border. But the store didn't have the wall-to-wall shoppers like the night before. Kerri Urdaz, 31, of McAllen loaded ice, water and batteries into her car, while her 2-year-old daughter Claire watched from the shopping cart.
"It wasn't too bad," Urdaz said of the last-minute shopping. "That's why we woke up and came in early before the rush."
Jesus Gil was lifting large coolers into the back of his pickup truck and had bought flashlights and batteries, bracing for the storm at both work and home.
"I'm just trying to be prepared," said Gil, who was in Houston in 2005 for the Hurricane Rita evacuation. He doesn't plan to leave this time, but bought extra gas just in case.
Maj. Jose Rivera of the Texas Army National Guard said troops were preparing at armories in Houston, Austin and San Antonio. Gov. Rick Perry called up 1,200 troops to help and issued the disaster declaration in the South Texas counties.
In the Gulf of Mexico, Shell Oil evacuated workers from oil rigs, but said it didn't expect its production to be affected by the storm.
Other areas are bracing for at least a tropical storm with warnings issued from Port O'Connor to San Luis Pass, south of Galveston in Texas and from La Pesca to Rio San Fernando in Mexico.
Mexican border towns near the Gulf coast were setting up shelters and soldiers were also being sent into Matamoros, across the Rio Grande from Brownsville, to protect against looting.
On South Padre Island, vacationers packed up their camps and headed for the mainland.
About 40 children and staff at a summer camp were heading north to San Antonio.
"We're not taking any chances with these kids," said Rabbi Asher Hecht, director of the Lubavitch Camp Gan Israel.
Just across the causeway in Port Isabel, residents were gathering supplies and boarding up windows. Not one to take chances, Larry Haines pulled out the plywood for the first time in years, boarding up his waterside art gallery.
"We're just worried about flying debris breaking through the windows," Haines said. "We're not too worried about storm surge and other things you get from a bigger storm, but we're going to board up anyway."
Also Tuesday, Fresenius Medical Care was preparing to close six dialysis clinics, which serve about 900 patients in the Rio Grande Valley.
Other parts of Texas, stricken by drought, watched Dolly expectantly, with as much as 4 inches forecast to fall by the time the storm's eastern edge sweeps across the region, said Texas A&M University's John Nielsen-Gammon, the state's climatologist.
About 20 counties in the northern part of South Texas -- which includes San Antonio and nearby counties to the north, south and east -- are behind in annual rainfall by between 12 and 16 inches, he said.
"If you get that much (rain) in two days there'd be flooding," he said. "Weather never gives you ideal stuff. This is certainly not going to be an exception to that. The best to hope for from this is a temporary reprieve from the dry conditions."
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