Brown is also planning a statewide tour to push his message for more tax revenue to save programs.
Brown already signed $11.2 billion in spending cuts, mostly to social services, leaving the state with a $15.4 billion budget deficit. He said Tuesday that Californians of all political persuasions have no appetite for billions of dollars in further cuts.
"I think ultimately, from everything I can tell, people don't want to make drastic cuts. They don't want to gut the university, gut public education, weaken public safety," he said. "But under our system ... the only way to get tax extensions is Republican votes. We must get those four votes."
A balanced budget revision is expected to make the May 14 deadline.
The governor says it will then be up to the state legislature to decide whether to pursue honest cuts to close the deficit.
The Associated Press contributed to this report.