The District of Columbia government is expected to show a $7 million budget surplus when the fiscal year ends Sept. 30, and the city's budgets for the next two years also are likely to be balanced -- signaling a definite end to more than a decade of deficit spending.

But while Mayor Marion Barry, who has said he plans to emphasize his firm handling of the city's financial crisis throughout his reelection campaign, apparently has solved the city's short-term fiscal problems, the major component of his long-range rescue package now appears imperiled on Capitol Hill.

The linchpin of the long-range plan is Congressional authorization for the city to issue up to $184 million in general obligation bonds to retire debts incurred before the current fiscal year, or to reimburse the city treasury for bills from previous years that have been paid out of current revenues. The remainder of the $388 million overall debt would be paid off by the city in $10 million annual increments.

Aides to Democratic congressmen who support the bond authority plan said this week that its chances for passage are 50-50 at best, while some Republican opponents predicted the measure won't even reach the House floor this year.

Rep. Stewart B. McKinney (R-Conn.), an influential member of the House District of Columbia Committee whose support is deemed essential to the bill's passage, said through a spokesman he intends to abstain on the vote.

Rep. Stan Parris (R-Va.), another committee member, said yesterday he disagreed with the city's plan to use a bond issue to pay off correct operating deficits "at a time when the American people are being asked to tighten their belts and do with less."

"I think the District of Columbia government is taking a very risky approach . . . instead of seeking further savings from existing programs," he said.

An aide to Del. Walter E. Fauntroy (D-D.C.), the chief sponsor of the measure, said, "Candidly, I would not view it as something that would fly through the House. McKinney is critical, and a lot of people will follow his lead."

One well-placed Republican source on the District Committee claimed that "no one (among the Democrats) is championing the city's cause," and that the legislation appears to be dead for the year.

Philip M. Dearborn, the mayor's chief financial counselor, acknowledged the possibility that the year-old plan could be either shot down or sidetracked in the House. In that event, Dearborn said, the city's hopes of acquiring financial respectability and access to less costly municipal bond markets would be dashed -- just as the 1982 campaign for mayor presumably would be getting under way.

Without its own bonding authority, the city government would continue to limp along, borrowing from the Treasury to cover spot cash shortages and paying a premium for long-term Treasury loans to finance capital improvements, such as building construction and street and sewer repairs.

This year alone, the city borrowed $80 million from the Treasury to offset short-term cash shortages. All $80 million must be repaid by the end of this month.

The beginning of the campaign would also coincide with the time when the city would begin to feel the brunt of the first round of Reagan administration cuts in federal grants for social programs.

Barry has already reduced spending for city services, to the chagrin of many neighborhood organization leaders, and he has angered many of the city's public employe unions -- some of whom supported his election in 1978 -- by reducing the public workforce by 12.5 percent, or 4,132 jobs in the last two years.

Tax increases would be the only way to avoid further cuts. In separate interviews this week, Dearborn and Budget Director Gladys W. Mack ruled those out.

"You can assume, considering it's an election year, that the likelihood of the mayor recommending and the City Council approving a tax increase next year are pretty slim," Dearborn said.

The House District Committee approved the bonding bill on July 14, after McKinney, the ranking Republican and usually a strong supporter of city efforts, reluctantly dropped his objections.

But McKinney and the three other Republicans on the 12-member committee have grown increasingly unhappy with the measure, according to one key congressional aide.

McKinney complained during hearings preceding the vote that Barry's proposal would "mortgage the future to pay for mistakes of the recent past." He said the city hadn't exhausted other avenues for raising the necessary funds, including selling off city-owned land (which the city now plans to do), ordering further cutbacks in government services and employes or raising taxes.

Another committee member, Rep. Marjorie Holt (R-Md.) contended through a spokesman yesterday that the proposal is fiscally irresponsible and "rather ludicrous," in light of the city's projected $7-million surplus.

Capitol Hill aides said that some Republican congressmen suspect that the city overstated its need for the bonding authority at hearings earlier this year.

"We were told that there would be some payless paydays this summer and the city would go under," one aide said. "Well, it's September and it hasn't happened."

Aides to Fauntroy and Rep. Ronald V. Dellums, (D-Calif.), chairman of the District Committee, said that that several extraneous issues -- including religious and civic opposition to the city's revised sexual assault code and opposition within the House D.C. Appropriations subcommittee's to the city's legalized lottery plans -- have diverted congressional attention from the bonding bill.

Dearborn said that some critics of the mayor's financial recovery plan were mistaken if they thought the city could produce a painless alternative to the bonding plan.

"Frankly we have not been able to find a good alternative, painless or otherwise," Dearborn said. "The city can't enter the municipal bond markets as long as it has that $184 million deficit on it's balance sheet."

In presenting his plan 14 months ago, Barry argued that once the city succeeded in getting a handle on its long term debt and achieved a suitable bond rating, it could end its reliance on the Treasury as its principal lender and seek more favorable borrowing terms in the private market.