Arrington Dixon, the independent-minded head of the city's legislature, took on Mayor Marion Barry one day last week on the issue of laid-off government workers. At a meeting of the District of Columbia City Council, Dixon introduced legislation to exempt laid-off workers who were being rehired from the city's strict residency requirement -- a position opposite the Barry administration's policy.

Dixon gave an emotional appeal that often harked back to his own boyhood in Southeast Washington. But when it came down to the votes, he could persuade only four of his council colleagues to join him. His bill failed on a 5-to-5 tie.

That episode on Tuesday was just the latest in a series of artfully choreographed movements by Dixon away from the mayor on crucial issues from the budget to city pay raises. Often frustrated, sometimes isolated by his own council, Dixon has been staking out distance well clear of Barry in what many political observers are viewing as Dixon's prelude to his eventual run for mayor, possibly as early as 1982.

Dixon is well aware of the constant suggestions that his opposition to Barry is political posturing. "I always look to the substance of what I've said, "Dixon said last week. "If there is substance to what I've said, then I dismiss that talk".

But there is a clear pattern to Dixon's emerging outspokenness against the administration, a pattern that became evident in mid-September when he began three days of hearings on the mayor's plan to borrow $215 million from the federal financing bank. Dixon referred to the mayor's financial bail-out proposals as a "phantom plan."

That same week in September, at the City Council meeting, Dixon continued putting the distance between himself and Barry, by introducing legislation to give city workers a full 9.1 percent pay increase. The mayor had already proposed a 5 percent pay increase, and Dixon himself conceded that the city did not have the funds available.

Despite an emotional pitch, to the cheers of the city workers packed in the council chambers, Dixon could rally only a single supporter on the council, and his bill failed 11 votes to 2.

Three weeks later, when Barry appeared before the council for a briefing on his newly unveiled 1982 budget, Dixon greeted the mayor by calling his new budget a "phantom document" wrought with a "blatant, obvious absence of information." But when the chairman looked around the dais for support, he found one of his colleagues accusing him of taking a "cheap shot" and another asking the chairman to " stop moaning and groaning."

Dixon maintains that when he comes out strongly against the mayor, he is attempting to preserve the autonomy of the legislative branch, and exercise a proper balance of power between the mayor and the council. "It is important to have some constructive tension," Dixon said. "The council is a new institution. We're still in the embryonic stage."

Legally and technically, the council has been gaining more of a role in the city's governmental structure -- especially in the budget process, which previously was the domain solely of the mayor. In the last year, the council has developed its own budget staff has given itself the power to review federal grant funds to the city has acquired a veto over short-term borrowing and has given itself the power to restrict the mayor from "reprogramming" -- or moving funds around -- with out council approval.

As chairman, Dixon has been out front, pushing and prodding the council to use its new authority to exert more influence in the governmental process. But he has often been frustrated in his efforts, and finds little support from his council colleagues, although the reasons vary.

Some say the chairman's problems rivaling Barry stem from Dixon's own particular brand of leadership on the council he has chaired since January, 1979.Dixon was elected chairman by defeating the controversial and outspoken former Council member Douglas Moore in a race all other competitors stayed out of to give Dixon a clear shot.

"Any chairman of the council is in a difficult position because as a representative of the legislative branch of government, you have to assert the authority of that branch," said one council member. "But you can't do it so you totally obviate cooperation with the executive. You have that built-in balance of power."

Several council members suggested that Dixon's efforts are sometimes thwarted because of his tendency to take on issues alone, from the dais, without first lining up support from his colleagues.

Council member Betty Ann Kane (K-At Large) said, "(Dixon's) new speaking out has not been accompanied by any increased skills in getting any votes. The problem that has plagued his chairmanship -- the difficulty in keeping in contact with council members -- is still there."

Another well-placed council source, referring to the residency exemption bill, said, "Nobody knew anything about that until he came up on the dais. People get tired of his showboating up there. If he had consulted his colleagues, he might have gotten something out of it."

In the District's short history of elective politics, many observers believe the council chairmanship is emerging as a primary launching pad for mayoral candidates. Next to mayor, the council chairman is the second-highest and most visible position in the city government. And the council's newly acquired powers in the budgetary process have really made it a coequal branch in many ways, more so than ever before.

Former Council Chairman Sterling Tucker used the chairmanship as his launching pad for the mayor's race in 1978, but was defeated in a close three-way race by Barry, then an at-large council member.

But Tucker, as chairman, did not face some of the problems that Dixon has today. For one, Tucker was one of the three most senior members of the council, having served on the old appointed council and having more seniority on the body -- and therefore the respect of experience -- than his colleagues.

Also, only two members of Tucker's council, Barry and Moore, were openly interested then in seeking higher office, and so Tucker had only two real rivals on the body for power and influence.

Dixon is a peer to most of the members on the current council, having served only one term -- and never having run at-large -- before being elected chairman. Also, since Barry launched his mayoral bid from the chairmanship of the finance and revenue committee -- and with the budget now occupying most of the recent council discussion -- the finance committee head has emerged as a force on the council independent of the chairman.

Because of Barry's council experience, and the close liaison with the Council that he has kept since becoming mayor, he is not as easy a target for criticism as former Mayor Walter Washington. As a council member, Barry prided himself on being able to deliver a seven-vote majority, and now as major he can still count on some council members' allegiance on key issues.

Dixon has said that if the District's three most highly visible elective offices -- the mayor, the council chairman, and the non-voting delegate in Congress -- were truly equal, then there would not be so much speculation about who was running for mayor. "There has to be more sharing of power," he said, "instead of having one branch trying to neutralize (another's) role."