Both say that they and many other officials are adamant about rebuilding New Orleans once this crisis is over.
"People cannot give up on the city as bad as this looks," the Academy Award-nominated actress told The Early Show co-anchor Harry Smith. "It's devastating and it's catastrophic, but I have also been around the city and there are pockets of the city that can come back quickly, and I want people to come back."
Clarkson had returned to New Orleans from the Venice Film Festival, where her movie with George Clooney, "Good Night And Good Luck," premiered.
She and her mother are trying to help people who are in harm's way. "God bless them," said the councilwoman, who represents the French Quarter. "They won't leave their houses, and many of them are holing up in attics. It's one of the things that has been very upsetting."
The councilwoman was with New Orleans Mayor C. Ray Nagin at the Hyatt hotel when Katrina hit and she stayed there until Friday.
"I saw the Hyatt for the first time yesterday and I can't believe anyone who was in that building is alive," Patricia Clarkson said. "But I must say, I am glad to be home with my family and I am fortunate that they are all fine and well."
Her mother stands behind Nagin's authorization of law enforcement officers and the U.S. military to force the evacuation of all residents who refuse to heed orders to leave the city.
"I am going out with some of those search-and-rescues today," Jacquelyn Clarkson said, "because I was going to try to convince these people they cannot sustain where they are, and their lives are in danger.
"They think the worst is over, but we have plenty to go. We have disease and the inability to get sustenance to them — food and water — and they have no sanitary facilities. They have to get out."
The West Bank, which is part of her district, is excluded from the mandatory evacuation.
"They have no flooding and they do have sanitary conditions and running water," she said. "However, the water pressure is low, so the fire risk is high, and we don't want people coming back in there, either. But for that part of town, it is not mandatory evacuation."
Once the city is dry, she said, officials will start a major cleanup project and then rebuilding will begin.