The D.C. City Council, faced with rising multimillion dollar deficits in the city's unemployment compensation fund, is expected to approve a proposal by Mayor Marion Barry that will cut benefits to jobless workers and increase unemployment taxes paid by businesses.

The proposal, which comes before the full council next Tuesday, would cut the maximum number of weeks that unemployed workers can collect city unemployment benefits from 34 to 26 weeks. Businesses would face a significant rise in unemployment taxes, with the heaviest increase falling on companies that traditionally have had the lowest unemployment tax rate.

The proposal would also eliminate unemployment compensation to people who have been fired. Under the current law, such people are eligible for reduced benefits after waiting several weeks.

If approved by the council, Barry's bill would take effect next month. It would not affect people now receiving unemployment benefits.

"We are facing a difficult situation . . . we don't have the money to do all the things we would like to do," D.C. council Chairman David A. Clarke said yesterday. Clarke and other council members said in interviews over the past few days that they expect the council to approve the bill.

Key business and labor officials, while not completely satisfied with the proposed changes, have nevertheless endorsed the proposal as necessary to the survival of the fund.

The District's unemployment compensation fund has a deficit of nearly $60 million. It has been insolvent for several years, but the situation has been compounded recently by high unemployment and federal restrictions imposed by the Reagan administration in the face of huge federal unemployment expenditures.

The federal government now requires the District and other local governments to pay interest on loans obtained from the U.S. Treasury to cover deficits in local unemployment compensation funds. The District must pay $2.4 million in interest for last year's loans, and is expected to pay $3.4 million in interest this year.

Washington's unemployment benefits are among the most liberal in the country. The city's $206 maximum weekly benefit for unemployed workers is the seventh highest in the country and well above the maximum weekly payments of $153 in Maryland and $138 in Virginia.

The maximum length of time that unemployed workers can receive benefits from the District--34 weeks--is one of the highest in the country, with most jurisdictions allowing only up to 26 weeks.

Local benefits can then be supplemented by up to 10 weeks of federal aid. Legislation authorizing the federal benefits expires next month, but proposals now before Congress would provide an extension.

Barry submitted his proposed changes to the council last month. Although the council's committee on housing and economic development, chaired by Charlene Drew Jarvis (D-Ward 4), made some revisions earlier this month, the basic proposal has remained intact and still has Barry's support.

Jarvis said yesterday that both business and union officials are to be commended for supporting the proposal.

John R. Tydings, executive vice president of the Washington Board of Trade, said the changes will be "very painful" and costly for local businesses, but represent a "very positive" step by Barry and the City Council to control unemployment costs and improve the city's overall economic climate.

Tydings said that once the deficit is erased, which District officials estimate will occur in 1986, the contributions from businesses would decline. Business leaders have long maintained that high unemployment costs in the District are a prime factor behind the relocation of D.C. businesses to the Maryland and Virginia suburbs and that they discourage businesses from moving here.

Joslyn N. Williams, president of the Metropolitan Washington AFL-CIO, said unions recognize that they must make concessions in light of the fund's large debt and the city's tight overall financial situation.

But Ron Richardson, a top official of the Hotel and Restaurant Employees Union here, has attacked the proposed changes as a "blatant sellout of the workers."

Richardson, who is feuding with Williams' group and who supported Barry's chief opponent in last year's race for mayor, opposes, among other things, the proposed cutback in the time period for receiving benefits.

Williams, whose organization is an umbrella group of labor unions that represent 250,000 workers, said that Richardson's hard-line stance is impractical. He said that the average length of time that D.C. jobless workers collect unemployment is 22 weeks, well below the maximum 34.

Costs to employers will rise as a result of a provision that would require employers to pay taxes on the first $8,000 that an employe earns, rather than the current $7,500. The proposal would also raise the minimum tax from 0.1 percent to 0.8 percent of the first $8,000 an employe earns. Under a complicated formula, the minimum tax is charged to those firms with the least unemployment.