Santa Barbara school officials on Thursday warned parents and employees that the state budget fiasco soon could lead to midyear bloodletting.

In a memo posted on the Santa Barbara School District’s Web site, Deputy Superintendent Eric Smith said the state budget shortfall, despite optimistic early estimates, could reach $10 billion.

As a result, Smith wrote, Gov. Arnold Schwarzenegger has told educators across the state to gird themselves for making as much as $4 billion worth of midyear cuts.

“We are entering a long dark tunnel, and we have no idea of when we will emerge from the other end,” Smith wrote. “We will know more when the governor’s budget proposal is presented in mid-January.”