Bush ordered flags flown at half-staff at all public buildings, military facilities, and embassies "as a mark of respect for the victims" until Sept. 20.
Local officials had predicted the death toll would reach into the thousands, and federal officials agreed Sunday.
"I think it's evident it's in the thousands," Leavitt said.
Chertoff said an untold number probably will be found dead in swamped homes, temporary shelters where many went for days without food or clean water, or even in the streets once the water is drained from New Orleans, which could take a month or more.
"I think we need to prepare the country for what's coming," Chertoff said on "Fox News Sunday." "It is going to be about as ugly of a scene as I think you can imagine."
New Orleans Mayor Ray Nagin told NBC News that the situation has been "a tragedy, a disgrace."
The Bush administration continued scrambling to counter criticism that Bush and his administration didn't move aggressively enough right after the hurricane swept through.
The White House quickly arranged another trip by Bush to the Gulf Coast on Monday, while the president and first lady Laura Bush paid a thank-you call on the Red Cross' disaster operations center and announced a White House blood drive.
"The world saw this tidal wave of disaster" hit the Gulf Coast, Bush said at the Red Cross center. "Now they're going to see a tidal wave of compassion."
Besides Rice, Chertoff and Leavitt, Defense Secretary Donald H. Rumsfeld and Joint Chiefs of Staff Chairman Gen. Richard Myers also traveled to the region Sunday.
"It's going to take many, many, many months and into years for this area to recover," said Rumsfeld, who took a helicopter tour of New Orleans, met with military personnel conducting search-and-rescue missions and visited a concourse where evacuated patients were being treated.
Rice _ the administration's highest-ranking black _ became its chief defender against charges that help, particularly to the disproportionately black and poor victims in New Orleans, came too slowly. "Americans don't want to see Americans suffer," she said in Alabama.
On television, Chertoff was omnipresent, dispatched by the administration to appear on all five Sunday news shows after FEMA Director Michael Brown's damage-control efforts met with little success last week.
Chertoff echoed the White House line _ saying the time to place blame will come later, but he also said federal officials had trouble getting information from local officials on what was going on. For instance, he said, they hadn't been told by Thursday of the violence and horrible conditions at the New Orleans convention center.