Four percent of CBT revenue is already dedicated to environmental programs. The amendment would reallocate that funding.
Under the amendment, funding for open space would increase to about $150 million annually beginning in 2019.
It would end the diversion of tax revenue toward water quality programs, hazardous site cleanups, and air pollution - to the chagrin of some environmental groups.
The Assembly, Senate, and environmental groups had been divided on a funding mechanism. But a spokesman for Assembly Democrats said Thursday that the chamber would take up a resolution passed by the Senate.
"The most successful program in state history is running out of money and out of time," said Jeff Tittel, state director of the Sierra Club. "This is the last chance and opportunity we have to save open space."
The Assembly must pass the amendment with a three-fifths vote on Monday to put the question before voters in November. It does not need Gov. Christie's signature.
The state has not dedicated stable funding to open space since voters approved $400 million in land-preservation bonds in 2009. That money has since been spent.