Casey Anthony's Attorneys Give Glimpse Into Defense Strategy

VIDEO: Casey Anthony faces trial in the death of her 2-year-old daughter,
WATCH Casey Anthony's Trial to Kick Off

Attorneys representing accused child murderer Casey Anthony revealed a glimpse of what may be their defense strategy Thursday as they attempted to prevent the Florida woman accused of the killing of her 2-year-old daughter Caylee from receiving the death penalty.

"Her lack of maturity, her lack of impulse control, history of sexual abuse, suffered from insomnia, nightmares, lack of parental guidance ... [her] mother and father failed to protect her as a child … [the] fact that she was verbally and emotionally abused," said defense attorney Ann Finnell.

Anthony's attorneys did not say who allegedly sexually abused Anthony, but chose to address her past with potential jurors Thursday as a possible defense -- or to find out whether she'd get a fair shot at life in prison versus the death penalty, if she is convicted.

Anthony is accused of killing her daughter, Caylee Anthony, who was last seen alive in June 2008. Anthony has pleaded not guilty to the charges.

Caylee's disappearance wasn't reported until July 2008, when Anthony told police she had not seen Caylee in nearly a month, since dropping her off with a babysitter.

Anthony was arrested and charged with murder in October 2008.

Her daughter's skeletal remains were found in December less than a mile from the home she and her mother shared with the toddler's grandparents.

The little girl's death was ruled a homicide of undetermined means.

Jury Selection Process

Throughout the jury selection process, defense attorneys must be careful not to make it seem like Anthony killed her daughter, but are attempting to ensure that they can place jurors who might be sympathetic to their client.

"The defense attorneys have two goals here. Number one: innocence. And number two: there is a penalty phase in this case. They want to make sure that if and when they get to that penalty phase, they can get jurors who might be sympathetic to their client," "Good Morning America" legal analyst Dan Abrams said.

Potential jurors have been subjected to a barrage of questions by the attorneys – from which television and news programs they watch to their feelings on the death penalty.

Every juror on a death penalty case has to be willing to say that they could impose the death penalty -- though it doesn't mean that they will ultimately choose that sentence, it is to ensure that if necessary, they could.

Lawyers for Anthony are also trying to convince a judge that the she was not properly read her rights and that key statements by Anthony should be thrown out of her upcoming trial.

Among the remarks that could be at risk are Anthony's statement to Florida police that her missing daughter was with a babysitter named Zenaida Gonzales. Police eventually determined that Anthony did not know a babysitter named Zenaida Gonzales.

Losing key testimony of this kind could make it difficult for prosecutors to get the conviction of first-degree murder -- and the death penalty -- that they are seeking.