At midnight tonight, the old fiscal year of 1977 will expire, and the District of Columbia will run out of money. But, like Old Man River, the city will just keep rolling along, mainly because there is little else it can do.

Blocked by an enery filibuster and other problems, including a dispute over the national policy toward federally financed abortions, Congress failed this week to enact a D.C. budget for the new fical year, which staris Saturday.

Beginning a new fiscal year without an enacted budget is nothing new for the city.

In the past, however, Congress has cured such a situation with a stopgap "continuing resolution" that permits the city to spend money at the previous year's pace pending final approval of a new budget.

This year, there are no plans for such a resolution - not yet, at least. That puts the District in the awkward position of having absolutely no legal power to agree to spend money on anything, but spending it anyway, hopeing it has the money by the time the bills arrive.

The District budget of $1.3-billion plus could be enacted by next week. It still faces Senate action and deliberations by a joint conference committee to resolve differences with the House version. TO become law, it must go to the White House for the President's signature.

It is the first time in memory that the District has entered a new fiscal year without either a budget or a continuing resolution. David P. (Pete) Herman, a retired District budget director, said it hasn't happened since at least 1940.

Comer S. Coppi, the current D.C. budget director, said he was awaiting official word from Capitol Hill before deciding a course of action. "In my judgement," Coppie said, lacking some congressional action today "the city would have no authority to obligate funds after (midnight Friday)."

There was no official ord, but Rep. George Mahon (D-Texas), chairman of the House Appropriations Committee, had some unofficial comments that eased Coppie's anxiety when relayed by a reporter.

The District's legal right to spend, Mahon said at the Capitol, "can lapse for a few days" without disrupting municipl services.

In other words, Congress will look the other way while the District disobeys the law against spending without congressional authority, just like District Police typically ignore congressmen's illegally parked cars.

"If we can't get a continuing resolution or an appropriation bill, then we have to look to comments like Mr. Mahon's," Coppie said, adding, "That's good news."

Obeyed strictly, the law would prohibit the District from burning any electric lights, or maintaining telephone service, or anything else for whihc it would get a future bill - a clearly impossible course for a complex modern city.

Just how the District got into this financial fix is a complicated story, and it tells something about the process that finance all the federal departments.

Just last week, President Carter endorsed a proposal to give the District budgetary independence by 1982, which probably would prevent the recurrence of such a situation.

The bulk of the District's proposals were submitted to Congress in February, but some important amendment - including a request to spend $27 million in start-up costs for a downtown convention center - did not reach the Capitol until the last week of July. By then, Congress was preparing to recess for the month of August.

Since returning early this month, both houses of Congress have been at odds over the convention center, with the House favoring it and the Senate Appropriations Committee opposed. Sen. Lowell P. Weiker (R-Conn.) blocked consideration of the budget bill ast week in a tactical move the hoped would enhance chances for approval of the project.

By the time Weicker gave his go-ahead, the filibuster over the Carter energy program had begun in the Senate, and the city budget was caught in a legislative traffic jam.

Now a further complication has arisen that effects the course of the District budget.

A joint Senate-House conference committee remains deadlocked over whether federal Medicare funds should be spent for elective abortions. That impasse is blocking the appropriation bill for the Labor and Health, Education and Welfare Departments, both of which also center the new fiscal year without a budget.

If a continuing resolution were offered in the House prior to the abortion conferees' agreement, it would involve Labor-HEW along with the District budget. And, one senior House member contended yesterday, such a resolution might fail because of the abortion issue.