Brown called on Democrats and Republicans to bring their best thinking forward to help close the state's $25.4 billion budget gap.
In his 14-minute address, Brown told lawmakers it would be "unconscionable" for them to block his request for a special election.
He targeted, Republicans who have constistently said they will block the move to put the proposal on the ballot, citing the civil unrest in Egypt and Tunisia to make the point democracy should be a guiding force on whether California should have a voice in his plan.
Brown wants a ballot measure this June that would ask voters to extend temporary tax increases, but Republicans have said they will not allow it.
"We need to break away from the failed status quo," said Assemblywoman Connie Conway (R-Tulare) in the Republican response. "We must cut spending, and we must do it now. The people have made it clear. They don't want higher taxes."
Conway said California's economy could get back on track by stimulating job creation in the private sector, but not by raising taxes.
California has the second-highest unemployment rate in the nation at 12.5 percent.
A recent poll shows Brown's call for a special election to extend tax increases for five years has public support.
He said without an extension of current taxes, the alternative is cutting education across the board and public safety.
It was Brown's eight career State of the State address.
The Associated Press contributed to this report.