They and Schwarzenegger want the federal government to find a way to undo the judge's order that has been reducing the water flow to save the fish.
Asked if he thinks they should just let the smelt go extinct, Schwarzenegger said, "No. …I think there is a better way of going."
He doesn't want to tarnish his environmental credentials - he's known as "the green governor." So he's trying to have it both ways.
Asked if he can have it all, he told Stahl, "Absolutely, you can have it all."
"Save the smelt?" she asked.
"It's just you got to recognize that it is a very, very complicated issue," Schwarzenegger replied.
Stahl spoke to Jeffrey Mount, founder of the Center for Watershed Sciences at the University of California, Davis. He says the smelt were once "incredibly abundant," but that very few of them are left."
Mount says that three quarters of the water shortages are caused by the drought, not the fish, and he has a message for the farmers: "Don't plant crops that have to have water every year. So some of the mistakes that farmers are making in that system is they're planting crops that can't be sustained in periods of severe drought. And Lesley, if there's one takeaway to have here, is the future for California is going to be dealing with scarcity. We have to adapt to basically chronic scarcity."
He does admit that the timing of the judge's order, in the midst of the drought, has made things worse.
"I mean, of all times to come along and try to save a little fish that big. People don't understand. They don't get it," Stahl remarked.
"Well, I wish they would ask beyond the little fish, because the little fish is essentially your bellwether. It's telling you, you have an ecosystem which is in dramatic decline," Mount said.
He points to the state's salmon population, which is so low that commercial fishing has been shut down for two years.
Asked what has gone wrong, Mount told Stahl, "We can't do it sustainably. You cannot currently meet the demand. Nowhere else on the planet can you point to a place which relies, for their water supply system, on an estuary."
An immense estuary, the Sacramento-San Joaquin Delta is where the state's main rivers meet the sea. The best way to get a sense of how vast it is is from the sky.
"This is it. This is the delta," Schwarzenegger told Stahl during an aerial tour of the estuary.
"The home of the famous Delta smelt that all the controversy seems to have bubbled up over," she remarked.
"Well it's the home of the smelt and all kinds of other species that people have been fighting over. And it's all happening right in this area," Schwarzenegger explained.