The court has made more than 20 previous rulings over more than two decades in the case, known as Abbott v. Burke. It has consistently found that the state needs to do more to educate children in 31 school districts, including Camden, Burlington City, Pemberton Township, and Gloucester City, where poverty is concentrated.
Christie, unlike previous governors, has taken a hard stance against what he sees as judicial meddling in matters that should be his and the Legislature's business.
Christie has cited the case as an example of why he wants to shake up membership of the state Supreme Court. He has said he might consider disregarding the court's ruling if he disagrees with it.
The case's latest chapter dates to last year's state budget. With onetime federal economic stimulus money gone, the state's total subsidies to schools were down about $1 billion. Even after the cuts, New Jersey provided nearly $8 billion in school aid, nearly a third of the state's total spending for the year.
Lawyers for the state said New Jersey could not afford more, adding that the cuts were deeper in wealthier districts. For the state budget that takes effect July 1, Christie has proposed an additional $250 million for all schools.
The Education Law Center, an advocate for children in the impoverished districts, sued the state. It argued that the state failed to subsidize schools at a level the court previously found acceptable.
A lower-court judge appointed by the Supreme Court to investigate found that the state would have to have given schools $1.6 billion more to have complied fully with the formula.
The law center has asked the court to order the state to meet the requirements of the funding formula.
Christie has said if that happens sharp cuts might have to be made to other areas of the state budget, such as aid to towns and hospitals. He said reinstating a higher income tax rate on people who earn more than $400,000 - something some Democrats have urged but he opposes - would only fill part of the gap.
Extra spending over the years for poorest districts has not helped much, Christie has said. Those districts get more than half the state's funding for schools, leaving other districts to rely mostly on property taxes to pay for schools.
The additional state money to the so-called Abbott districts has meant upgrades to school buildings and free preschools in New Jersey's low-income cities. But more than two decades after the first Abbott rulings, there is still a big gap in test scores between most of the low-income schools and other districts.