“A good deal of the surge of revenues that we have seen since the beginning of the year is the result of higher-income individuals being able to realize some of their gains at the end of 2012,” said H. D. Palmer, the director of external affairs for the California Department of Finance. “We don’t believe it is prudent to budget on the capital gains. It wasn’t that long ago when we had the same experience during the dot-com boom. We don’t want to see that movie again.”

In one particularly revealing moment, the office of the independent legislative analyst — which has a history of scolding governors for unrealistically optimistic budget projections — dismissed Mr. Brown’s figure as pessimistic, saying extra revenue was closer to $4.4 billion. The report undercut Mr. Brown just as he and lawmakers moved into the final stages of budget negotiations, and it empowered Democrats and social service advocates eager to reverse budget cuts.

“I support the governor’s call to pay down more debt aggressively, I support the notion of a rainy-day fund,” said Darrell Steinberg, the president pro tem of the Senate. “But I also believe that we have an obligation to make some limited but important investments in restoring some of what has been lost over the last four or five years.”

Vanessa Aramayo, the director of California Partnership, a group of organizations pushing for social service spending, said Mr. Brown was deliberately understating the state’s financial health.

“The governor is attempting to leave a legacy of solving our state budget crisis,” she said. “But he’s doing so on the backs of poor people in the state.”

Other Democrats said the Legislature should proceed with caution, given the history of financial gyrations in California and, no less important, concern that any perception that Democrats were on a spending spree could prove politically damaging to the party.

John A. Pérez, the speaker of the Assembly, said that he supported putting revenues into a contingency fund, but that some of the money should go to increase spending on programs like college scholarships for middle-class students.