In many ways, California’s troubles are rooted in strict regulations against rising property tax rates, a landmark constitutional amendment that voters approved in 1978 and that led to a taxpayer revolt throughout the country. The measure cut and capped property taxes for existing owners, limiting them to 1 percent of valuation and making it more difficult for municipal governments to use climbing property values to fill their coffers. The initiative spawned several other voter-approved budget regulations that limit the State Legislature’s ability to shape the budget, including setting minimum spending levels on public schools.

Mr. Brown and his allies — including John A. Pérez, the speaker of the State Assembly — say that the biggest problem now is the state’s dependence on capital gains, which fluctuate wildly amid boom-and-bust cycles. Republicans have long argued for scaling back capital gains taxes and pushing more of the burden to middle-class residents, an idea many Democrats find repugnant.

“Why would we tax those who can most afford it at a lower rate — that’s laughable on its face,” said Mr. Pérez, who has promoted the idea of a rainy-day fund for months. “My main concern is that we do this now, while the recession is still fresh in our memories. We all know what it was like to preside over very, very painful cuts. This is our best effort to stop this from happening again.”

Several recent polls show that voters enthusiastically back rainy-day fund proposals, and Mr. Brown is convinced that his bigger challenge is winning over the State Legislature. While Democrats may object to more budget restrictions, Republicans are more supportive of a rainy-day fund proposal already on the ballot that was negotiated by former Gov. Arnold Schwarzenegger in 2010 — his last year in office and the last time the Republican Party had any control over state finances. That proposal would essentially set a spending cap, which Mr. Brown and other Democrats say is too limiting.

The State Assembly could vote on the governor’s proposal before negotiations on the annual state budget begin next month. But Darrell Steinberg, the leader of the State Senate, has made it clear that he is not rushing to meet the governor’s demands, saying instead that the focus should be on restoring cuts and addressing major shortfalls in pension funds.

“This has implications for generations to come,” Mr. Steinberg said.

He added, “I’m concerned about a double-whammy of a lot of money going to a rainy-day fund and a separate appropriation going to pay down debt, which would leave little room for infrastructure, public safety, education and other key investments that have been cut deeply.”

The state has had a rainy-day fund for nearly a decade. But payments to it can easily be waived by a governor, and it has mostly gone unfunded since it began. Under Mr. Brown’s plan, any increase in capital gains tax would be set aside in the fund, which could also be used to pay down long-term debt.