SACRAMENTO — When Jerry Brown became the 34th governor of California in 1975, he was a young and impetuous bachelor who slept on a box spring and took pleasure in defying political convention. He was the vanguard of the left, the face and spirit of a new generation of a state that — politically and culturally — was proudly distinct from the rest of the nation. He has been such a fixture ever since that it seems impossible to imagine California without him.

Now, as Mr. Brown enters the final 12 months of his second tour as governor, and as he prepares to deliver his final State of the State speech here on Thursday, he has become the face of the old order — admired for his long stewardship, but also seen as a roadblock for some younger Democrats who have impatiently awaited change.

This is a decidedly more liberal class of Democrats, on issues ranging from single-payer health care to the impeachment of President Trump, and many of them have long said the time has come for Mr. Brown’s generation to step aside.

“He is a middle-of-the-road sort of guy and if I’m being perfectly honest, he is not completely in touch with the way the majority of folks in California feel,” said Kimberly Ellis, a Democratic leader from the Bay Area who lost a fight last year to lead the state Democratic Party. “In many ways, with respect to single-payer and other issues, he and others play the safe role — the conservative role.”