Their flight inland has been slowed by traffic jams stretching up to 100 miles (160km), with fuel shortages reported.
Texas is due to bear the brunt of the storm but forecasters say its path may shift east, upping the risk heavy rains may test New Orleans' flood defences.
President George W Bush is due to visit Texas to see the preparations there.
The state has called on the federal government to put 10,000 troops on standby for search and rescue work.
The Gulf Coast from Louisiana as far west as Mexico is on alert, with officials warning Rita's course remains unpredictable.
In other developments:
Mr Bush will fly to Texas on Friday to "get a first-hand look at the preparations... and to show our support for the first responders as they get ready", said White House spokesman Scott McClellan.
The president, criticised for the federal government's response to Hurricane Katrina last month, told reporters in Washington that "officials at every level of government" were "preparing for the worst".
According to the National Hurricane Center, Rita weakened on Thursday to a Category Four, but was still carrying winds of 140mph (220km/h) on Friday morning.
HOUSTON FACTS
The storm remains "extremely dangerous", being at least as powerful as Katrina and threatening 370 miles (600km) of coastline.
Houston's busy airports will close at noon local time (1700 GMT) ahead of Rita's expected landfall late on Friday local time.
A mandatory evacuation order in the island city of Galveston was rapidly observed and 90% of the city's 57,000 residents had left by Thursday afternoon.
The escape from Galveston has been gruelling, the BBC's Daniela Relph reports, with those who left spending much of the past 24 hours stuck in traffic jams in stifling humidity.
Many have been left stranded on the roadside, out of petrol, low on water and food, waiting for help from the police or the Texas National Guard, our correspondent adds.
"My stomach is in a knot and I'm distracted as I go through the house making preparations"
To the north of the city, a traffic queue up to 100 miles (160km) long was reported as people headed inland in temperatures reaching 37C (100F).
"We've got no gas. We're dealing with heat exhaustion, heart attacks," Sheriff Randy Smith of Waller County, Texas, told a local television station.
Scores of hospitals along the main evacuation routes out of Houston closed their doors to new patients on Friday after being swamped by people suffering heat exhaustion, AFP news agency reports.
Mexican alert
In neighbouring Louisiana - which may be worse hit than expected if the storm veers east - Governor Kathleen Blanco urged people to leave the south-western coast, already battered by Hurricane Katrina.
She estimated that between 300,000 and 500,000 people would go.
Engineers have been seeking to bolster the floodwalls in New Orleans, which were overcome by Katrina's storm surges.
Some estimates say even a few inches of rain would overcome the weakened flood defences.
Mexico has not evacuated its coastal state of Tamaulipas where tropical storm conditions are predicted.
However, the state is on a "yellow alert" in case Rita should veer west, away from Texas.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~40~RS~)
