As Democrats unveiled their ambitious Green New Deal to fight climate change Feb. 7, a controversy erupted over the role of nuclear power that threatened to undermine the entire effort.

A fact sheet distributed by the office of progressive newcomer Alexandria Ocasio-Cortez, a Democratic representative from New York, said there was no room in the nation’s all renewable-energy future for nuclear plants.

But the reference caught many off guard and back-peddling ensued.

Giselle Barry, a spokeswoman for Sen. Ed Markey,...