On the weighty agenda of the United States Senate, which is fond of calling itself "the world's greatest deliberative body," the budget of the District of Columbia usually is assigned something less than the highest priority.

All this week. Sen. Patrick J. Leahy (D-Vt.) has been waiting to call it up - the first bill to be managed on the Senate floor by the new, young chairman of the Senate District Appropriations Subcommittee.

First the measure was stalled by Sen. Lowell P. Weicker Jr. (R-Conn.) in a dispute over the District's plan to build a $110 million convention cneter near downtown in Washington.

Leahy is against the project. Weicker is for it. Weicker acknowledged yesterday that he was holding up the bill temporarily in hope of gaining strategic advantage when he tries to persuade the full Senate to support the center.

Nobody knows when he'll get the chance.

Along with important national measures, the D.C. budget got stuck this week in a sort of legislative Bermuda Triangle, awaiting the outcome of a filibuster against part of President Carter's energy program.

Now comes Sen. Ernest F. Hollings (D.-S.C.), looking for a way of getting the Senate to approve an urgent $1.4 billion in disaster loans to farmers in the nation's drought-stricken Southeastern states.

He decided to attach it as a rider to the only appropriation bill pending before the Senate - the D.C. budget for the 1978 fiscal year, which starts next Saturday.

Suddenly yesterday it became the tail that was wagging the dog. The D.C. budget, which hardly anybody noticed up to now, became important far beyond the city's borders.

"We're concerned it's not moving" said an aide to Sen. Lawton Chiles (D-Fa.), whose farmer constitutuents stand to get many of those disaster loans.

The tactic is all right by him, Leahy said, because time is running short for the District budget's enactment, and any help in getting it moving is welcome.

If the bill is not approved in final form by both houses of Congress before the end of next week. Leahy said, it is distinctly possible that the District may be left without a budget until January at the soonest.

The reason, he told a reporter, is that Congress is pushing for adjournment by the Oct. 15 target date announced Thursday by Senate Majority Leader Robert C. Byrd (D-W. Va.).

The Senate must act meantime on such items as energy, the federal debt ceiling, social security financing and a catch-all appropriation bill to run a list of federal programs.

That doesn't mean that the District would be left without any money, Leahy said. It would be kept running by a so-called "continuing resolution," under which the city could spend at the same level as in fiscal 1977.

But - and Leahy stressed this point - there would be no money for such projects as the convention center.

Weicker, also interviewed yesterday, insisted that his tactic should improve the convention center's chance for approval in the Senate.

The project is in an unusual parliamentary situation.

The House has approved spending $27 million of start-up costs for the project, but a parliamentary maneuver last week by Rep. Robert E. Bauman (R-Md.) removed the source of the money - a loan from the U.S. Treasury.

The Senate Appropriations Committee in recommending its version of the budget to the full Senate, has sided with Leahy in omitting the convention center entirely. Weicker and Sen. Thomas F. Eagleton (D-Mo.) have said they will ask teh Senate to reverse that action.

Weicker said he has refused up to now to agree to a time limit for Senate debate on the District budget. Under procedures enforced by Byrd as majority leader, this blocked consideration of the measure.

However, Weicker said, he will agree to a time limit after the House acts - probably Monday - on a separate bill to restore the city government's right to borrow money from the U.S. Treasury for the convention center and other construction projects.

With uncertainty over the project's financing removed. Weicker said its chances of approval in the Senate should improve.

"I want to make it clear. I'm not trying to delay the bill, Weicker said. "I want to get it passed."