Mayor Marion Barry and City Council Chairman Arrington Dixon unloaded heavy verbal artillery on one another yesterday in an exchange that Barry suggested was a preview of a challenge to him by Dixon in the mayoral election of 1982.

Dixon branded Barry's proposed 1982 city budget a "phantom document" marked by the "blatant, obvious absence of information on how well department heads have controlled their spending under your administration." He said he was "tempted to recommend" that the Council, which received the budget less than a week ago, send it back to Barry for more information.

Barry, admitting he was upset by Dixon's salvo, said the chairman was "playing with the lives of the citizens" to make political capital out of the budget review process. He said Dixon had not even read the budget but was "relying on some staff who just came aboard a few weeks ago."

Telling Council members at a three-hour briefing that the budget contained more information about city spending than any other under home rule, Barry said that "it's not my fault if certain members of the council like the chairman haven't read it and ask preposterous questions."

His voice rasping from a cold and his schedule skewed by the long session, Barry did not attempt to hide his irritation at Dixon's tactics. He said he was open to suggestions for improving the budget and that the council was "not going to get from me resistance for the sake of resistance. I welcome ideas, but if it's political, if it's for 1982 and running for mayor or something, I'm going to reject it."

The exchanges between Barry and Dixon enlivened an otherwise desultory briefing of the council by Barry and his aides about the proposed 1982 city budget. The discussion produced no information about the mayor's $1.5 billion spending program for the fiscal year beginning next Oct. 1 that was not included in the budget document, except that Barry was forced to concede that a tax increase would be necessary to finance any salary increases for city workers unless Congress increases the annual U.S. payment.

Barry's position is that the 1982 budget is balanced without tax increases, but there is no money in it for salary raises. If negotiations with unions representing the city's 32,000 employees lead to a city committment to raise their pay -- as they surely will -- the mayor proposes to finance the increases out of $76 million in additional federal payment that he hopes to get from Congress. Without that, he said, a tax increase would be needed.

Dixon is a Democrat like Barry but did not run with him in 1978. During the last several weeks, Dixon has been staking out staking out a position well clear of the mayor's on city financial matters. He opened the session by reading a statement saying that the proposed 1982 budget was "vague if not misleading."

He said that "the public is left in the cold on what exactly are our liabilities, who our creditors are, and when they expect to be paid. Several thousand men and women have been terminated. Frankly, I am beginning to ask, why?" He questioned whether the money saved by laying off city workers was being used for debt service or to "finance nonpersonnel, discretionary cost overruns."

If Dixon is going to use the budget review process to score political points on Barry, he may not have the support of other council members. With the entire council present, no member endorsed his remarks. Councilwoman Polly Shackleton (D-Ward 3) called his statement unfortunate and "a cheap shot." John A. Wilson (D-Ward 2), chairman of the committee on finance and revenue, said it would "do this legislature a great deal of good if we would stop moaning and groaning about what the mayor sent to us and decide what we want to send back to the mayor."

Dixon persisted. He said he had in fact read the budget thoroughly and would be "derelict in my duty" not to question Barry's proposals.