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By Peter Henderson

SAN FRANCISCO, Dec 31 (Reuters) - California Gov. Arnold Schwarzenegger on Wednesday proposed closing a $42 billion budget gap by shortening the school year, borrowing nearly $5 billion, raising the sales tax and tapping the state lottery.

But even if legislators agree with proposals to cover the next 18 months, California might run out of cash in February and have to defer some payments and resort to IOUs -- promises to pay.

California, the most populous U.S. state, is a social trendsetter that is also at the leading edge of local governments failing to come to terms with an economic crisis.

The state expects unemployment of more than 9 percent in 2009 and 2010 on top of a mortgage crisis that has already dented tax revenue.

"We are facing a major crisis," Finance Director Mike Genest said, showing the plan to reporters. "These are really difficult choices. These are substantial tax increase. These are major program reductions, and even with all of that we couldn't quite get there," he added, explaining the decision to try to tap the bond markets for $4.7 billion in July.

In addition, to make up the nearly $42 billion shortfall, a sales tax hike and other revenue increases would bring in $14.3 billion, spending would be cut $17.4 billion and $5 billion would be raised through the state lottery. That would leave about $95.5 billion in the state's main general fund for the budget year starting in July.

The new plan covers the remainder of the current budget year, which ends in June, and the 2009-2010 year that starts July 1 -- although the $4.7 billion debt issue would not be paid back until the following year.