A state Assembly committee planned a hearing Tuesday on the Republican-sponsored measure. It cleared a Senate committee earlier this month.
The ban would only be in place when workers are present in the construction zones. Drivers could still place cell calls to report emergencies.
State law currently bars drivers from texting while driving. New drivers on a probationary license are barred from using a cellphone while driving.
Under the construction zone ban, violators could face fines of between $20 and $40 for a first offense and up to $100 for a second offense.