The measure is due to go before the Appropriations Committee.
Lawmakers say it's very difficult to hold drivers criminally accountable when they kill or injure someone while talking or texting. They can, though, be sued for damages in civil court.
The Assembly's Law and Public Safety Committee recently approved the bill. And a Senate panel approved a similar measure last month.
Earlier this year, a state Senate panel voted to increase fines for texting and talking while driving. Repeat offenders would also face a driver's license suspension and points against their driving record.