The idea is to give workers a chance to care for either a sick relative or new child.
The Senate budget committee today pushed forward a measure to let employees take up to six weeks off with pay.
The measure faces opposition from businesses and Republicans.
The New Jersey leave would be paid through a charge against weekly wages that legislative officials estimate would cost workers about $33 per year.
Workers who take leave would get two-thirds of their salary, up to $502 per week.