But California, given its size as the largest state, has long held outsized influence regardless of who the governor is. It is far from certain, too, whether Mr. Newsom will succeed in his goal of shaping the party’s agenda; while candidates are talking about similar policies, they are not holding up California as the example. And it is too early to say how far left the party will be pulled during the presidential campaign.

Neera Tanden, a former aide to Hillary Clinton and president of the Center for American Progress, a research and policy organization in Washington, D.C., placed Mr. Newsom’s administration in a national context. “The way I look at Gov. Newsom is he has the opportunity and responsibility to demonstrate how progressive governance can work,” she said.

“I think there will be a big question hanging over the national debate over the next two years about whether Democrats can deliver on prosperity,” she said. “There will be lots of attacks from conservatives. Being able to deliver a progressive agenda against a backdrop of a state that is growing, that is still having innovation, is really important.”

Ms. O’Leary is among a number of aides working for Mr. Newsom who previously worked for Ms. Clinton or President Barack Obama. She acknowledged the criticism that Mr. Newsom’s administration has taken a scattershot approach to governing, but said that many of the initiatives are about tackling the problem of how expensive life has become in California.

“We are at a moment in time where people will remember what he did or he will be part of the problem,” said Ms. O’Leary. “We now have over 60 percent of young people in California say they cannot afford to live in California. They can’t imagine how they are going to make it or stay in California.”

Daniel Zingale, who worked for three former governors — Mr. Brown during his first period in office in the 1970s, Gray Davis and Mr. Schwarzenegger — before becoming a communications aide to Mr. Newsom, said he had urged his new boss to focus his attention on a few key issues.

“I was just pointing out that there was a political advantage to having signature issues,” he said. “That’s just a political fact. But he made a more compelling argument that we live in these times of the fierce urgency of now, on a whole bunch of issues.”