Mayor Marion Barry has softened his previously adamant stand against an increase in District of Columbia taxes as his aides find it increasingly difficult to close a massive revenue gap this year and draft a balanced budget for fiscal 1984.

Barry recently pledged that his administration would head off projected overspending and revenue shortfalls totaling $110 million this year without raising taxes or laying off city employes. He also gave his budget director, Gladys W. Mack, marching orders to prepare a fiscal 1984 budget proposal that doesn't include a tax increase.

But late last week, after returning from a National League of Cities conference in Los Angeles, Barry declined to unconditionally rule out proposing a tax increase until after he reviews the budget materials Mack is expected to submit next week.

"You never have a Sherman-like statement about anything," Barry said Friday at the District Building. "But I doubt I'm going to change my mind about anything."

If a tax increase proves to be necessary, city officials said they would be least willing to try to raise income, property or sales taxes, which generate about 75 percent of the District's local tax revenues, and which, not incidentally, are most politically sensitive.

The administration probably would focus its efforts on obtaining new and higher user fees to offset administrative costs, as well as increasing other minor taxes.

The mayor may also press the City Council to approve a $14.6 million tax-increase package that he introduced this year but which gained little support. That package includes a gross-receipts tax on utilities, which would replace a sales tax.

Although the projected revenue shortfall for the current fiscal year is only about 5 percent of the District government's overall operating budget of $1.9 billion, city officials are required by law to have a balanced budget.

The mayor's reluctance to propose a tax increase to deal with the problems is underscored by new figures released by the city's Department of Finance and Revenue showing that the city's tax burden on middle-income and upper-income families is among the top 10 in the nation, and is the heaviest in the metropolitan area.

The figures, which confirm established trends, show that a D.C. family of four making $25,000 a year pays an average of $2,146 annually in taxes -- tenth in the nation. A family of four making $50,000 pays an average of $4,914, which ranks sixth in the U.S.

"I will not embrace tax policies that drive people and businesses out of town and thereby reduce the base of income which supports needed city services," Barry said in a recent letter to the City Council outlining the extent of the problem.

But Barry has placed his top budget and financial experts in a bind with his public pledges, which include a promise not to cut spending for education, corrections, or police and fire protection.

As one of Barry's top aides explained: "It's a real problem. They [budget officials] are squeezing everywhere they can."

Mack said last week she will be able to comply with Barry's dictum in revising the current fiscal 1983 budget and drafting the fiscal 1984 budget.

If necessary, she said, some entire city programs no longer deemed essential may be eliminated.

Jeffrey Humber, the acting director of the Department of Finance and Revenue, said his staff is considering a wide range of methods for boosting revenue collections, short of raising tax rates.

But City Council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee, said the problems cannot be overcome unless Barry and the council work together to "formulate some sort of package we all can support."

Wilson said last month that he would not propose any new tax increases unless Barry agreed to support the increases first.

"He wants somebody who will raise the taxes and take the heat for it," Wilson said then.

By last week, however, Wilson had modified his position. "We have to get out of the fall-guy syndrome," Wilson said. "If he doesn't do it, I'll have to do it. As far as I'm concerned, nothing is sacred."

The potential $110 million deficit that Barry disclosed early last month results from a $51 million slump in tax revenues caused by the recession and an estimated $58.9 million in unforeseen spending, primarily for social services like Medicaid and public assistance.

The downward estimate of revenues, including the loss of $24.6 million in sales and use taxes and $16.8 million in income taxes, was based primarily on a forecast of only a modest recovery in the area's economy during the next nine months.

City officials said this projected revenue loss will be partially offset by a $24 million increase in the proposed federal payment that is still pending in the Congress.

Meanwhile, property tax revenue will remain stagnant, officials say, because of the slump in the real estate market.