How one governor plans to cope with budget deficit

California, which decided last Nov. 2 to ''let George do it,'' now knows how its new governor, Republican George Deukmejian, plans to corral the state's unprecedented $1.5 billion budget deficit.

Perhaps taking his cue from another Republican who once governed California and now resides in the White House, fiscal conservative Deukmejian has proposed a plan for deficit financing.

In his first ''state of the state'' message Jan. 10, Governor Deukmejian proposed that $750 million of the projected fiscal 1983 deficit be eliminated by various freezes and program cutbacks. Another $750 million would be borrowed from private sources, to be paid back during the next fiscal year starting July 1. The state government already has borrowed $400 million from California banks to pay its current bills, and payback of $200 million of that is due in February.

Leaders of the Democratic majority that controls the state Legislature, chided by the governor in his speech for behaving ''like a spendthrift who wastes his inheritance,'' immediately indicated they would oppose the Deukmejian plan. They want to raise taxes rather than make further program cuts. But the new governor, standing by a campaign pledge, provides for no new taxes in his budget proposal.

John Vasconcellos, chairman of the Assembly's Ways and Means Committee, said he would ''not be a party to mortgaging the future.'' Calling the Deukmejian proposal ''morally irresponsible, fiscally irresponsible, and just plain stupid, '' Mr. Vasconcellos said his committee will not even discuss the budget plan.

The governor, who was state attorney general for the past eight years, insists that his proposal ''is consistent with the constitution and laws of California.'' The state constitution requires that the governor submit a balanced budget for each fiscal year. Although it does not specifically require that the budget be in balance at the end of the year, the law has up to now been interpreted to mean that.

To effect $750 million in savings, the governor would reduce spending for most state programs by 2 percent. He also would cut $108 million from allocations to local governments, $75 million from education, and $75 million from health and welfare programs.

Deukmejian, who evoked a new theme - ''the Common Sense Society'' - in his inaugural and state of the state addresses, stakes the success of his proposals on a national and state economic upturn producing a growth rate in 1983 of 2.2 percent (the White House has projected 1.4 percent growth in the gross national product). He also says he believes that loosening the grip of government regulation of business in California will help stimulate an upturn.