SACRAMENTO, CALIF., NOV. 28 -- Gov. George Deukmejian (R) said yesterday that California's alarming budget crisis is worsening and announced that he is calling the state legislature into special session to deal with the mounting fiscal mess.

The outgoing governor said he expects the special session, which will begin Monday, to produce no new taxes.

"I rather doubt seriously that the legislature is going to want to propose or support any major tax increases, and I don't think that's the answer to the problem," he said.

Leaders of the Democratic-controlled legislature already have indicated that they have no intention of bargaining with the lame-duck Deukmejian, who has made fiscal austerity the cornerstone of his administration, preferring instead to deal with Gov.-elect Pete Wilson (R).

But Deukmejian said the state's bond rating is in jeopardy and swift action is imperative.

"When a business or a family suddenly experiences a decline in income, they don't wait two, four or six months to take action to reduce expenses," Deukmejian declared. "The responsible ones would act now."

The special session of the state legislature would coincide with a brief ceremonial session already scheduled Monday. But Deukmejian said he hopes lawmakers will consider a program he has crafted to ease the budget crunch by $1 billion.

He said figures released last week by a state finance panel showing that California faces a $4.3 billion deficit in the 1991-92 fiscal year may be conservative. A $5 billion gap is possible, Deukmejian warned.