ANNAPOLIS -- Baltimore County Executive Roger B. Hayden today asked the county's legislative delegation for either a 10 percent increase in the piggyback income tax, or the proceeds from a one-penny state sales tax increase to avert dramatic local budget cuts next year.

Mr. Hayden said that under the best circumstances, the county faces a $14.4 million deficit in the current budget year and a deficit of $34 million to $48 million in the fiscal year starting July 1, depending on which of the legislative plans under consideration is adopted.

The effect, he said, would be public school classes as large as 38 children each and the loss of 900 vacant county positions beyond the 1,000 already eliminated. He also told the county's delegates that no new teachers will be hired next year to teach the 4,000 new students the county expects in September, and that an estimated 450 current teaching jobs that become vacant by September will not be filled.

In addition, county workers will not receive a cost-of-living pay increase or step increases next year.

Raising the county's piggyback income tax from 50 percent to 60 percent would give the county $42 million next year. And returning a 1-cent increase in the state sales tax to county coffers would provide $55 million, he said. They are the only two possibilities that would produce enough money to keep the county from slowly self-destructing, Mr. Hayden said. He stressed that the new money would merely prevent further damage, but not provide enough to restore this year's cuts.

The continuing recession, he said, has reduced county revenues $27 million under estimates for this fiscal year. Most of that, about $19 million, is from lower income-tax revenues.

"We cannot be boxed out of options," Mr. Hayden said. "Even if we have a handle on that $48 million [deficit], we still have done some draconian things," he added. "We've cut everything. Road repair and paving is cut down to almost zip."