But Democrats say they don't want to adopt the governor's proposals to reduce spending on safety nets that help children, the disabled and the elderly.
The state is facing a $24.3 billion deficit.
"We are going to make government more efficient, and we're going to live within our means," Schwarzenegger told the NBC Station in Sacramento in a one-on-one interview at the Capitol. "That is the most important thing here in this budget."
The Republican governor, who emphasized the severity of California's budget woes on Tuesday during an address to legislators, said the cuts will "redefine" California, adding the government can't promise things it cannot deliver.
Schwarzenegger has outlined a series of cuts that include an additional $5.2 billion reduction to public schools, laying off 5,000 state workers and further cutting the pay of another 200,000. He has proposed eliminating welfare for 500,000 families, terminating health coverage for nearly 1 million low-income children and closing 220 state parks.
Schwarzenegger added that he is not open to the idea of higher taxes. He said voters' rejection of five budget-related ballot measures during the May special election made it clear they do not support any tax increase.
The governor and state Controller John Chiang have warned that the state is facing possible functional insolvency. While California cannot technically go bankrupt, the state is very close to running out of cash to pay its bills.
In a letter to legislative leaders last week, Controller John Chiang warned that California will run out of money to pay its bills on July 29. He called on lawmakers to pass a balanced budget by their June 15 constitutional deadline so the state can access short-term loans in a tight credit market. The state's new fiscal year begins July 1.
State revenue has continued to plummet as residents have reduced spending and the state's unemployment rate soared to 11 percent. Democratic lawmakers and the Schwarzenegger administration have even inquired about having the federal government give California a loan guarantee, an unprecedented step that is seen as a way for the state to lower its borrowing costs.