Energy Secretary Rick Perry has invoked doomsday scenarios to argue that the shuttering of nuclear and coal-fired power plants will put the U.S. power grid at risk, leaving elderly Texans without air conditioning and New York’s financial center vulnerable to a crippling blackouts.

“I do not want to get a phone call from someone whose grandmother has died in their home because the electricity went off in August where our days are 105 to 110 degrees,” Perry told House lawmakers...