Florida's House OK'd it last week.
The measure's supporters say it would be the toughest law of its type in the nation.
It would shift some focus to prevention, and require schools to take disciplinary action to stop physical or verbal abuse that isn't averted.
According to the House and Senate staffers, the legislation provides lots of legal cover for school authorities to intervene with the parents of both bullies and victims. It forces schools to notify both sets of parents of the bullying, steps that are discouraged at the moment, due to privacy issues.
David Tirella, an attorney who recently won a $4 million jury verdict in a school bullying case in which the school was sued for providing inadequate protection for the victim, is pushing hard for the Florida measure.
He told Early Show co-anchor Harry Smith Thursday "we have to" get the bill approved and signed by the governor. "I worked on cases the last three years. And I know there are Floridians that are being bullied right now, today, I'm sure there are students in class in Florida and throughout the state that are in fear.
"We know there's a problem. We know what the fix is. The social scientists have been telling us since Columbine how to fix it. Florida now has a bill. If it becomes law, it will help students -- 2.5 million students. We've got to fix the problem today."
What's being done now to curb bulling "doesn't work," Tirella says. "Not all teachers -- teachers are great. There are some teachers and administrators that will not step up to the plate and protect the students. Right now, lawyers and judges have to get involved. This law, if it becomes law in Florida, will put the focus on the prevention. We don't want the victimization later. We don't need the lawyers. We want the therapists. We want the teachers to step in."
Tirella admits he's "heard about it" from colleagues who point out that lawyers could have fewer cases to pursue if the bill becomes law but, after he won his recent case, "I received calls from all over the country from parents as recently as the other day asking to get involved, thanking me for getting involved.
"We have a problem, we have an answer. Florida has an answer. If we pass this law, we have an answer. I want to do something. I want to help these kids before they're injured. That's what I want to do. ... That's why I'm here to help."
CBS News correspondent Mark Strassmann visited with two school bullying victims in Florida and their families, and reported on their struggles.
To see Strassmann's report and Smith's interview of Tirella, click on the arrow in the image below.