Engineers in this swamped city toiled at pumping out flood waters Tuesday after fixing a significant levee break, but officials warned of the grisly scenes that would likely be uncovered.

"It's going to be awful, and it's going to wake the nation up again," said New Orleans Mayor Ray Nagin (search), who estimated Monday that the city's death toll could reach 10,000.

Nagin ordered any remaining residents who've been refusing to leave to get out of the city, reminding them that the flood waters carry toxins and disease and it was not safe to stay.

The pumping was already having an effect, Nagin said, estimating that the city had gone from being 80 percent underwater to 60 percent underwater. He said the water levels were lower than he'd seen since Katrina hit last Monday.

"I'm starting to see rays of light all throughout what we're doing," the mayor told reporters Tuesday.

The pumping began after the Army Corps of Engineers (search) used rocks and sandbags over the Labor Day weekend to finally plug the 200-foot gap that let water spill into New Orleans — which is below sea level — in the aftermath of Hurricane Katrina (search).

Meanwhile, President Bush vowed to launch an investigation into "what went right and what went wrong" in the hurricane recovery effort and why it has taken so long to send help to the ravaged Gulf Coast. Congress pledged to undertake a separate investigation.

Senate Democrats estimated the government's share of relief and recovery may top $150 billion, and a congressional official said Tuesday that Bush plans to ask for $40 billion to cover the next phase of the operations.

But the president said the probe would have to wait because for now, the focus needs to be on continuing to get the situation under control.

"A lot of people are playing the blame game," Bush said Tuesday. "We need to solve problems. We're problem solvers. ... If things went wrong, we'll correct them."

Bush, whose administration has been under fire for the federal government's sluggish response to the disaster, said he was sending Vice President Dick Cheney (search) to the region on Thursday. The president has toured the devastated area twice.

Nagin said it would take three weeks to remove the water and another few weeks to clear the debris. It could also take up to eight weeks to get the electricity back on.

"I've gone from anger to despair to seeing us turn the corner," he said on NBC's "Today."

Still, the mayor warned that what awaits authorities below the toxic muck is gruesome.

Walter Baumy, a Corps manager in charge of the engineering job, said it will take 24 to 80 days to drain the city.

Exactly how long the job will take depends on a number of factors. Among other things, the condition of the pumps — especially whether they were submerged and damaged — is not yet fully known, the Corps said. Additionally, the water is full of debris, and while there are screens on the pumps, it may be necessary to stop and clean them from time to time.

Lootings and shootings have also plagued New Orleans, but some order had been restored by Tuesday.

New Orleans Deputy Police Chief Warren Riley said officers were getting the city — which descended into lawlessness in the week following the hurricane — back on solid ground.

"The city is on lockdown," Riley told reporters Tuesday. "We have control of this city. We're expanding that control as the waters recede."

Twenty arrests were made overnight Monday out of the 150 total arrests that have been made since the storm, according to Riley.

He said that morale was beginning to build again. The police department was sending some officers on vacation out of town so they could get away from the horrors and rest.

"Things are getting better," he said.

New Orleans Fire Chief Charles Parent said the fire department had been rebuilt and relocated across the Mississippi in the Algiers section of the city, and that all personnel were accounted for.

But putting out the various blazes across the city has proven difficult.

Early Tuesday, fire broke out at a big house in the historic Garden District, a neighborhood with many antebellum mansions. National Guardsmen cordoned off the area as firefighters battled the blaze by helicopter. It was one of at least four roaring across New Orleans Tuesday.

"The fires are getting a good head start on us because of delayed detection," Parent said. "By the time anyone sees it, it's grown to a magnitude that makes it difficult to fight ... We have to improvise as much as possible."

He said the crews fighting the fires, many of whom have lost everything themselves, have been remarkable in their endurance and strength.

"I have never been more proud of a group of men and women in my lifetime," he said.

The Pentagon, meanwhile, began sending paratroopers from the Army's storied 82nd Airborne Division to New Orleans to use small boats, including inflatable Zodiac craft, to launch a new search-and-rescue effort in flooded sections of the city.

Maj. Gen. William B. Caldwell IV, division commander, said about 5,000 paratroopers would be in place by Tuesday.

Efforts to evacuate holdouts were stepped up, with boat rescue crews and a caravan of law enforcement vehicles from around the country searching for people to rescue.

"In some cases, it's real easy. They're sitting on the porch with their bags packed," said Joe Youdell of the Kentucky Air National Guard (search). "But some don't want to leave and we can't force them."

Nagin warned: "We have to convince them to leave. It's not safe here. There is toxic waste in the water and dead bodies and mosquitoes and gas. We are pumping about a million dollars' worth a gas a day in the air. Fires have been started and we don't have running water."

At the same time, the effort to get the evacuees back on their feet continued on several fronts.

Many people across the country opened their homes to those left homeless by the tragedy, and donations continued to pour in.

Patrick Rhode, deputy director of the Federal Emergency Management Agency (search), said evacuees would receive debit cards so that they could begin buying necessary personal items. He said the agency was going from shelter to shelter to make sure that evacuees received cards quickly and that the paperwork usually required would be reduced or eliminated.

"We're eliminating as much red tape as humanly possible," Rhode said on ABC's "Good Morning America."

The Air Force late Monday concluded its huge airlift of elderly and serious ill patients from New Orleans' major airport. A total of 9,788 patients and other evacuees were evacuated by air from the New Orleans area.

A plan to move some evacuees from the Houston Astrodome to cruise ships was postponed because many didn't want to go.

In St. Bernard Parish (search), officials expressed frustration that federal aid, slow to reach New Orleans, was even slower to get to outlying areas.

"This is Day 8, guys. Everything was diverted first to New Orleans, we understand that. But do you realize we got 18 to 20 feet of water from the storm, and we've still got 7 to 8 feet of water?" said Ron Silva, a district fire chief. "If you had dropped a bomb on this place, it couldn't be any worse than this."

In addition to help from other Louisiana and Alabama departments, a Canadian task force of firefighters and police arrived four days after the storm, St. Bernard Fire Chief Thomas Stone said.

"If you can get a Canadian team here in four days, U.S. teams should be here faster than that," Stone said. Pointing to two large oil refineries, "When they're paying $5 to $6 a gallon for gas, they're going to realize what this place means to America."

The frustrations also were being felt along the Mississippi coast, where people who have chosen to stay or are stuck in demolished neighborhoods scavenge for necessities.

Some say they will stay to rebuild their communities. Others say they would leave if they could get a ride or a few gallons of gasoline. But all agree that — with no water or power available, probably for months — they need more help from the government just to survive.

"I have been all over the world. I've been in a lot of Third World countries where people were better off than the people here are right now," retired Air Force Capt. William Bissell said Monday. "We've got 28 miles of coastline here that's absolutely destroyed, and the federal government, they're not here."

The scope of the misery inflicted by Katrina was evident Monday as President Bush visited Baton Rouge and Poplarville, Miss., his second inspection tour by ground.

"Mississippi is a part of the future of this country and part of that future is to help you get back up on your feet," Bush told 200 local officials.

While in Louisiana, Bush tried to repair tattered relations with the state's Democratic governor, Kathleen Blanco (search), while also praising relief workers. Blanco played down any tension.

"We'd like to stop the voices out there trying to create a divide. There is no divide," she said. "Every leader in this nation wants to see this problem solved."

Meanwhile, former Presidents Bush and Clinton got smiles, hugs and requests for autographs when they met with refugees from Hurricane Katrina — but it was Bush's wife who got attention for some of her comments.

Barbara Bush, who accompanied the former presidents on a tour of the Astrodome (search) complex Monday, said the relocation to Houston is "working very well" for some of the poor people forced out of New Orleans.

"What I'm hearing, which is sort of scary, is they all want to stay in Texas. Everyone is so overwhelmed by the hospitality," she said during a radio interview with the American Public Media program "Marketplace." "And so many of the people in the arena here, you know, were underprivileged anyway, so this is working very well for them."

The two ex-presidents, who teamed up during a fund-raising effort for victims of last year's Asian tsunami, announced the creation of the Bush-Clinton Katrina Fund.

"We're most anxious to roll up our sleeves and get to work," said former President George H.W. Bush (search). "It will take all of us working together to accomplish our goal. This job is too big for any one group."

U.S. Health and Human Services Secretary Mike Leavitt (search) declared a public health emergency for Texas, saying it would speed up federal assistance to help almost 240,000 storm evacuees — the most of any state.

In New Orleans, Deputy Police Chief Riley estimated that fewer than 10,000 people were left in the city. Some simply did not want to leave their homes, while others were hanging back to loot or commit other crimes, authorities said.

Nagin said the city had the authority to force residents to evacuate but didn't say if it was taking that step. He did, however, say that water would no longer be handed out to people who refuse to leave.

The leader of troops patrolling New Orleans declared the city largely free of the lawlessness that plagued it in the days following the hurricane. He lashed out at suggestions that search-and-rescue operations were being stymied by random gunfire and lawlessness.

"Go on the streets of New Orleans — it's secure," Army Lt. Gen. Russel Honore said to a reporter. "Have you been to New Orleans? Did anybody accost you?"

In neighboring Jefferson Parish, some of its 460,000 residents got a chance to briefly see their flooded homes, and to scoop up soaked wedding pictures and other cherished mementos.

"I won't be getting inside today unless I get some scuba gear," said Jack Rabito, a 61-year-old bar owner whose one-story home had water lapping at the gutters.

FOX News' Catherine Donaldson-Evans and The Associated Press contributed to this report.