Caylee's body was found in December, and Casey, 23, has been charged with first-degree murder in her daughter's death.
In an exclusive interview with Early Show co-anchor Maggie Rodriguez Wednesday, Cindy and George Anthony said they don't think Casey should accept a plea deal, even though prosecutors just announced they're going to seek the death penalty in the case.
And George discussed a suicide attempt in the wake of all the developments surrounding his family.
Casey has pleaded not guilty. Her trial has been tentatively set for October. She was arrested last October.
Casey says she left Caylee with a baby sitter in June, but she didn't report Caylee missing for a month. Cindy was the first to call authorities, in July, to say that she hadn't seen Caylee for a month, and said her daughter's car smelled as if it had had a dead body in it.
A utility worker found Caylee's body last December in woods near where she lived with her mother and grandparents.
"We can't think about what's to come," in light of word the death penalty will be sought, Cindy told Rodriguez. "She hasn't even had her trial yet. Casey is presumed innocent, and, you know, we can't think about that right now."
"I don't really believe that her defense team is going to do anything to jeopardize anything in the future for her," George said. "So ... we have to wait and see what plays out. I don't believe that's going to happen with her."
Both answered with a firm "No" when asked if they'd encourage Casey to accept a plea deal.
"Absolutely not," Cindy said. "I don't think Casey will take a plea deal. Casey is not going to admit for something she hasn't done. We love our daughter. We stand behind her. We know what kind of mother she was."
"I don't think it's possible for my daughter to hurt anyone," George said, flat-out. "And she wouldn't definitely hurt her own child. I mean, my gosh, I've seen the love every single day that she had for her. She took care of her being with us. So, I mean, she wouldn't hurt her." He then got all choked up.
Why, Rodriguez wanted to know, did Cindy tell authorities Casey's car smelled like a dead body had been in it?
To that Cindy and George's lawyer replied, "Maggie, those are issues that are going to come up at trial. And they're anxiously awaiting that. And there's been so much pretrial publicity that's going to affect the ultimate outcome and her ability to get a fair trial. So the questions that have to do with the statements that they gave, they want to wait and tell the truth in front of a jury and let a jury decide."
"She's presumed innocent," Cindy pointed out. "I think the truth will come out at trial, and that's what we have to wait for. You know, the defense is going to do their job. We're confident that they're going to do their job. And, you know, they'll be able to see for themselves that it's -- there's more to it."
If Casey did commit the crime, how harsh should her punishment be?
"Again, you know, we want -- we want the truth," Cindy said, "but, again, we have to wait for everything to come out in trial."
Rodriguez gently said to George, "A little more than a month after (Caylee)was found dead, you had a very difficult moment. You almost took your own life. You ready to talk about that now?"
"I can talk some about it," he responded. "I mean, to try to keep your family together no matter what, to have so much put on you every single day, to be scrutinized, to be -- have people come at you at so many different directions like protesters at our house and stuff. All that weighs on you after awhile. I mean, to think how they tried to destroy my wife. Tried to destroy my son. Came after my daughter. Said negative things in such a way that I'm going to protect my family no matter what. And got to the point on that one day that there is just so much a person can take. I mean, sure that was the wrong direction to go in, and i know that. And i want to talk to more people about that kind of stuff. You can't give up, even though the days get very hard for you. There's other ways. There's people to talk to besides your own family. People you can reach out to and talk. They're going to be there for support to help you."