The District of Coumbia government, which rolled up a $105 million budget deficit last year, will finish the current fiscal year with a surplus of about $7 million, according to projections released yesterday by city officials.

It would be the first time since the 1960s that the District ended a fiscal year with a genuine surplus of revenues over expenditures.

Only four months ago, the same officlas who sat smiling at yesterday's news conference had said that the city might incur a deficit of up to $60 million this year. They later revised the figure to $30 million and promised Congress that they would eliminate the gap by Sept. 30, the end of the fiscal year.

The figures released yesterday show that the city government is still overspending its budget, but the overspending is more than offset by skyrocketing tax revenues. Fueled by inflation that is driving up prices and incomes, tax revenues will exceed midyear projections by $29 million.

If the city does actually end the fiscal year with a surplus, it will be a major political achievement for Mayor Marion Barry going into an election year and will enhance the city's standing with a skeptical Congress.

But it will not nearly solve the District's overall financial problems. The city still has a cumulative cash deficit of $184 million from prior years, and needs additional money from Cognress to cover salary and pension commitments for l982.

Moreover, expenditures are still rising faster than revenues and that means the same austere measures that helped produce the currently projected surplus -- could continue for another three years, said Phillip M. Dearborn, financial counselor to the mayor.

The House is scheduled to vote Monday on a bill to raise the annual federal payment to the District by $36.6 million, to $336.6 million. That measure has the support of the Reagan administration, but if it should fail, a new round of tax increases and service cutbacks would be inevitable.

The announcement that a surplus is likely this year should help the bill's supporters convince skeptics that the District is being managed efficiently.

All of Mayor Marion Barry's top financial managers, grinning at the rare opportunity to hand out good news, met with reporters at the District Building to announce the city's financial position as of June 30, three-quarters of the way through the l98l fiscal year.

"We said we would balance the budget this year, and this shows we are doing it," said City Administrator Elijah B. Rogers. "This should dismiss the myth that the people in this government are irresponsible and can't balance the budget. The city is in good hands."

What is happening this year is the exact opposite of the municipal spending patterns that prevailed in the 1970s and created the deficit. In those years, the District usually stayed within the spending ceiling set by Congress, but incurred deficits because of revenue shortfalls. Now the city is spending more than authorized by Congress but coming out ahead because of rising revenue.

In several years during the last decade, the city wound up with what was technically a cash balance on its books. But those balances were misleading because bills due during that fiscal year had been rolled over into the next.

In l978, for instance, former mayor Walter E. Washington's administration left office with a $40 million surplus on the books. But it also had accumulated $10 million in upaid bills that year, for a net annual budget deficit of $80 million.

This time, the city checkbook has a positive balance that will cover all expenditures incurred this year, city officials said yesterday.

Total general fund expenditures for l98l are now projected at $1.462 billion, against revenues of $1.469 billion, leaving a $7 million surplus. Since some city agencies are still spending more than their departmental budgets and further trims are possible, Rogers said, the final surplus could actually be larger. Whatever the amount, it will be used to pay off part of the $184 million deficit, he said.

The agency where most overspending is projected is the public school system, which anticipates a $5.8 million deficit. Budget Director Gladys W. Mack said yesterday that Floretta McKenzie, the new superintendent, had promised Barry to try to reduce that, and Mack said she thought it could be done without the furlough of teachers planned for September.

The city's Water and Sewer fund, which is calculated separately, is running a $9 million deficit, but Mack said that would be overcome by rate increases already planned for this fall. Only the exact size of the increases remains to be determined, she said.