NEW ORLEANS--Anxious evacuees scattered across America clamored to come home Tuesday after New Orleans was largely spared by Hurricane Gustav, but Mayor Ray Nagin warned they may have to wait in shelters and motels a few days longer.

The city's improved levee system helped avert a disaster like Hurricane Katrina, which flooded most of the city, and officials got an assist from a disorganized and weakened Gustav, which came ashore about 72 miles (116 kilometers) southwest of the city Monday morning. Eight deaths were attributed to the storm in the U.S. after it killed at least 94 people across the Caribbean.

But New Orleans was still a city that took a glancing blow from a hurricane: A mandatory evacuation order and curfew remained in effect. Electric crews started work on restoring power to the nearly 80,000 homes in New Orleans -- and more than 1 million in the region -- that remained without power after the storm damaged transmission lines that snapped like rubber bands in the wind and knocked 35 substations out of service.

"We have a massive caravan of crews coming to the city and they should be here this morning to fix the rest of the power outages," Nagin said on CBS "Early Show."

The city's sewer system was damaged, and hospitals were working with skeleton crews on backup power. Drinking water continued to flow in the city and the pumps that keep it dry never shut down -- two critical service failings that contributed to Katrina's toll. The FAA said the city's airport was expected to reopen at 7 p.m.

Gustav was downgraded to a tropical depression early Tuesday, and mandatory evacuation orders were lifted for three Southeast Texas counties.

The storm's maximum sustained winds decreased to near 35 mph (56 kph) as it puttered toward northern Louisiana and east Texas. Up to 8 inches (20.3 centimeters) of rain was expected and flood warnings were posted.

Nagin cautioned that Tuesday would be too early for residents to return to New Orleans, but their homecoming was "only days away, not weeks."

Crews would comb the city Tuesday to fully review the damage, Nagin said, with the goal of having residents return beginning late Wednesday or Thursday. Retailers and other major companies could start sending workers Wednesday to check on their locations, he said. Buses are in place and ready to bring residents back with instructions to drop them off as close as possible to their homes.

The state and city took pride in a massive evacuation effort that succeeded in urging people to leave or catch buses and trains out: Almost 2 million people left coastal Louisiana, and only about 10,000 people rode out the storm in New Orleans.

"I would not do a thing differently," Nagin said. "I'd probably call Gustav, instead of the mother of all storms, maybe the mother-in-law or the ugly sister of all storms."

But thousands of people were strained by sleeping in cots in gymnasiums and convention centers, far away from their homes and wondering when they could go back. Fights broke out at an overcrowded shelter in Shreveport. Doctors worried about medications running out and seven people were hospitalized, all in stable condition.

"People are desperate. They don't know if they are going to have a place to go home to," said Emma McClure, 37, who was at the shelter with her three children, three sisters and some 20 nephews. "They had three years to plan this and now I wish I had stayed in the city like I did during Katrina."

Though the big city was spared, Gustav devastated parts of Cajun country, destroying homes and flooding parts of the mostly rural, low-lying parishes across the state's southeastern and central coast that are also home to the state's oil and natural gas industries.

Four evacuating Louisianans were killed in Georgia when their car struck a tree. A 27-year-old Lafayette man was killed when a tree fell on his house as the storm whipped through, and an Abbeville couple was killed when a tree fell on a home in Baton Rouge. A woman from Jefferson was killed Monday when her vehicle ran off Interstate 10 and struck a tree.

Roofs were torn from homes, trees toppled and roads flooded. A ferry sank. Telephone service was spotty at best. Parts of the Mississippi Gulf Coast were isolated by flood waters, and Gov. Haley Barbour urged residents not to return to their homes until Wednesday.

More than 50 patients had to be evacuated overnight from two small community hospitals in central Louisiana after the storm knocked out their generators, according to Richard Zuschlag, chief executive of Acadian Ambulance. The patients were taken to two Lafayette hospitals.

Gov. Bobby Jindal said he heard reports of widespread damage across Terrebonne, Lafourche and St. Mary parishes. Crews were expected to fan out and in search of injured or killed people with helicopter crews.

To the east of the city, Jindal said state officials were planning an aerial tour on Tuesday to gauge damage to Port Fourchon, a vital energy industry hub where huge amounts of oil and gas are piped inland to refineries.