Environmental groups who helped launch a bipartisan House climate-change caucus two years ago are debating whether it’s worth saving.

Several groups that helped form the Climate Solutions Caucus met Nov. 8 to begin discussing what the future may hold for the informal House coalition, two days after the election that helped Democrats take control of the House swept away some Republican members.

Some environmentalists want the caucus to disband, noting that its Republican members barely resisted their party’s attacks on...