Attorneys for the groups are scheduled Wednesday to make oral arguments before a panel with the U.S. Nuclear Regulatory Commission during a hearing in Albuquerque.
The panel will determine which groups have standing and which objections will be considered as part of the case.
New Jersey-based Holtec International has applied for a license to construct the facility about 35 miles east of Carlsbad. It would be capable of storing as much as 120,000 metric tons of high-level radioactive waste.
Opponents have concerns about the project’s legality, the safety of transporting the fuel across the country and potential environmental effects.