The push comes as we learn new details about John Albert Gardner.
Court documents released to the San Diego Union Tribune show that he had a high grade point average and a high IQ. He held jobs as a lifeguard and as a ride operator at a Santa's Village.
His ambitions were to become a math teacher or a police officer.
Gardner, a convicted sex offender, is the sole suspect in King's murder, but he pleaded not guilty in court. The Rancho Bernardo teenager vanished Feb. 25. A body that is believed to be hers was found in a shallow grave in the park where she went jogging last week.
A 10-year-old probation report on Gardner states that a psychiatrist described him as having "significant predatory traits" toward underage girls. This report, released in court Tuesday, was prepared in Gardner's 2000 sentencing after he pleaded guilty to committing lewd acts on a 13-year-old girl. The girl was Gardner's neighbor.
Also in the report, the psychiatrist recommended that Gardner receive a mandatory maximum sentence. Instead, Gardner served five years on a six-year sentence. He was on parole for three years, then he was discharged with no tracking.
Gardner is also a suspect in the death of another teen, 14-year-old Amber Dubois from Escondido, who disappeared more than a year ago. Dubois' remains were found March 6 west of Pala Temecula Road approximately 25 miles from the girl's home.
After news that Amber's remains were found, administrators at her high school Monday brought in extra counselors to work with the students as necessary.
More than 1,000 people gathered at a candlelight vigil held to honor Dubois Monday night.
At the vigil, Amber's father pleaded for stronger laws.
"We as parents and a community need to make a change for the protection of our children," said Maurice DuBois, Amber's father.
"We know he is a child molester, we know he is violent, so how can this happen again?" said Lena Smyth of Santa Clarita.
Smyth heads Mother's Against Sexual Predators. She finds her answer by reviewing Gardner's record.
She found that Gardner committed his offense before Jessica's Law, a measure that helps track sex offenders and prohibits them from living near parks and schools.
Tuesday, an assembly member wanted answers from the Department of Corrections.
"We have been told that his entire field file has been destroyed, and they say this is consistent with their policy to destroy files one year after the person goes off parole," said San Diego Assemblyman Nathan Fletcher.
Smyth sounds the alarm for parents, pointing out that existing measures are filled with gaps, and there are other offenders like Gardner who were convicted before Jessica's Law.
"You can't apply the law retroactively but you can start categorizing child offenders as a more violent predator so we can start treating them as such in the system," sad Smyth.
The call for reform starts anew.
"Please take a minute, for every tear shed for Amber and Chelsea," said Amber's father at Monday night's vigil. "And come back tomorrow and take just as many minutes of action in our fight to protect our children."
Legislators will be assessing all the laws on the books. They say the search for solutions will not come easily or quickly.
AP contributed to this report.