The Legislature is expected to vote on the replacement measure next week. It would then supersede the measure already slated to go before voters in the general election.
The governor's office announced the deal jointly with all four Democratic and Republican legislative leaders. GOP support was essential because a ballot measure requires two-thirds votes in both houses of the Legislature, and Democrats have lost their supermajority in the Senate because three members of their party have been suspended after being ensnared in legal trouble.
Assembly Minority Leader Connie Conway said the deal that emerged Thursday reflects long-standing Republican priorities.
"It will ensure that money is actually saved, that it cannot be siphoned off to grow government, and that we will have resources to pay down debt and protect core priorities in tough years," the Republican from Tulare said in a statement.
Republicans also wanted to ensure that extra tax revenue during good years would not be siphoned off to create new, ongoing programs that the state could not afford when the economy turned sour.
The measure now on the ballot, Assembly Constitutional Amendment 4, grew out of a 2010 bipartisan budget compromise that included then-Gov. Arnold Schwarzenegger. That version creates a rainy day fund equal to 3 percent of the state's general fund.
The new version increases that to a maximum of 10 percent, which would be funded primarily through additional revenue from capital gains taxes during boom years. Part of it would be dedicated to paying down state debt and liabilities, estimated at $340 billion.
Transfers to the rainy day fund could be suspended and additional withdrawals could be made during a recession, but only within certain limits. That was a priority for Democrats, who wanted flexibility to tap the money when needed during a rough economy.
"While we certainly don't wish to return to the past, we cannot stagnate in the present either," Senate President Pro Tem Darrell Steinberg, a Democrat, said in a statement. "Instead of stockpiling money while ignoring looming debt, this smarter approach locks the state into saving and attacks our wall of debt and unfunded liabilities."