UPDATE 1-California's May jobless rate hits record 11.5 pct

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SAN FRANCISCO, June 19 (Reuters) - California's unemployment rate jumped nearly half a percentage point in one month to a record 11.5 percent in May, and Governor Arnold Schwarzenegger on Friday warned the economy would not recover quickly.

Led by a drop in government jobs -- a reflection of the state slashing its own payroll to try to cope with a mounting budget gap and the possibility it will run out of cash, the May rate was nearly 2 percentage points ahead of the national 9.4 percent rate, the California Employment Development Department reported.

California's May rate of 11.5 percent compared with a revised 11.1 percent in April, 6.8 percent a year earlier and the previous record of 11.2 percent set in March of this year.

"A full recovery will not happen overnight -- it will take time, which only further underscores the need to continue the economic stimulus measures I fought for in the February budget," Schwarzenegger said in a statement aimed at pressuring lawmakers to hammer out a budget deal. (Reporting by Peter Henderson; Editing by James Dalgleish)