It was ironic that at about the same time last week that a Senate subcommittee was eliminating the city's coveted convention center proposal from the 1978 budget, most of the local elected leadership of Washington was getting ready to fete former Washington Redskins quarterback Sonny Jurgensen at the District Building.

There is no certainty that a strong city presence at the markup session where the bill was under consideration would have changed the outcome. Some city leaders said the subcommittee, headed by Sen. Patrick J. Leahy (D-Vt.), had made up its mind well before the votes were taken.

"It doesn't make such differnce on mark-up," said Mayor Walter E. Washington. "You can't even talk."

But the fact that the mayor, City Council Chairman Sterling Tucker and other key city leaders were fiddling with Sonny while the convention center plan was burning, underscored one of the peculiar situations of D.C. city government.

Despite the fact that this city is more dependent than perhaps any other in the nation on the actions of Congress, no one in city government is assigned the fulltime - or even regular - task of lobbying on Capitol Hill.

The term itself often has an ugly connotation. It evokes images of cloakroom deals and back-alleys bargains. In fact, it is influence-peddling for hire, and a practice on which good government advocates frequently frown. It also includes the practice of keeping informed on what is in the works, often before it is made public.

Apparently it helps get the job done. About 65 to 70 cities have some type of Washington office or retain someone to represent them in Washington, according to the National League of Cities.

In addition, says Dick Cherry, director of the league's "Man in Washington" service, just about every mojor - and semi-major - local municipality lobbies its state legislature. The District doesn't have one of those. But some of the things which Congress does for the city - like establishing local taxing authority and approving projects like the convention center - are done for cities and countries by their state lawmakers.

"After all," Cherry says of the state-city relationship, "that's where they get their charter, that's who determines their taxing authority and sometimes how much they pay their firemen."

Neither the mayor nor the City Council assigns anyone the task of regularly pushing the city's position on the Hill. Why not?

"I don't know. I've never had that question asked before," says Alan Grip, press secretary for Council Chairman Sterling Tucker. "That's not to say it would be a good or bad idea. It just never came up."

Sam Eastman, the mayor's press secretary, think the absence of a lobbyist keeps the city's image clean. This way, Eastman says, "what we do is all out front."

Just what the city did in the line of lobbying for the convention center, which Washington business and government leaders had jointly touted as a godsend to the city's faltering downtown economy, is difficult to determine.

Grip said Tucker had personally talked with at least "a couple" of members of the subcommittee that scrapped the plan. The mayor repeatedly refused to say if he had talked personally to any congressman about the plan.

What city leaders belive is best is to deal with the staff of the subcommittee and to make good presentations at hearings and on paper. "I don't like the word lobby. I hope to give definition to what the city's needs are," said Budget Director Comer S. Coppie, the city's principal contact with Congress on the budget. "The important question was whether the city had made its case for the convention center. I think the answer to that question is in the affirmative."

But there are others who believes there would have been some value to city leaders being present in the room so Leahy and others would have had to look them in the eye and say no to the convention center plan. Other people besides committee members can be heared at mark-up sessions. Cherry said, and besides the presence of top city leaders has a symbolic value.

The city certainly doesn't intend to change its pattern of operations in a last ditch effort to save the convention center plan, or at least if they do, it will not be talked about.

When asked by a reporter if he planned to personally talk to any members of Congress to urge passing the convention center plan, the mayor said, "I can only tell you that we're going to continue to fight. I always get some personal contact in."