The D.C. Department of Employment Services says that dismal economic conditions will soon force the city's Unemployment Compensation Trust Fund into a $33.8 million deficit. To prevent that, the department says, the city might have to reduce the time period for which people can receive unemployment checks.

Matthew Shannon, acting director of the department, told the City Council's committee on housing and economic development that the fund is becoming insolvent because more people are unemployed and they are taking longer to find new jobs, drawing money out of the fund faster than it can be replaced.

"In 1980, we processed 720,000 weeks [of] claimed [benefits], and paid $88 million," Shannon told the committee Thursday. "Through November 1982, we have processed 867,000 weeks claimed and paid $118 million."

Shannon said his department projects a $33.8 million deficit in the fund by March 1983, based on the fact that the department has already had to borrow $16 million from the federal government to cover the period from October through the the end of the year and projects the need to borrow $17.8 million more for the period between Jan. 1 and March 31 of 1983.

"We will not run out of money for the fund," Shannon said yesterday. "But we will have to continue to borrow if the problem is not addressed."

Compounding the financial burden of more loans is the fact that a federal act that took effect last April requires states and the District to pay 10 percent interest on loans taken after that date. During the recession of the '70s, the city had to borrow $73.5 million from the federal government to make the trust fund solvent, Shannon said, but those loans were interest-free. He said interest on the city's current loans would be $13.1 million.

Shannon said Mayor Marion Barry will make a formal recommendation on ways to alleviate the deficit. Options under consideration include tightening benefits by capping the maximum weekly benefit check at its current level of $206 and reducing the maximum number of weeks that a person can receive checks from 34 to 26.

Other suggestions include raising revenues for the fund by increasing the minimum tax rate or increasing the taxable wage rate of the city's employers.

"This is a critical situation that we have an obligation to address," said council member Charlene Drew Jarvis (D-Ward 4), who chairs the housing and economic development committee. "Everybody has to take their lumps."