At least six of the 13 members of the D.C. City Council, saying that Mayor Marion Barry is trying to usurp their power, plan to counterattack by exercising more oversight control over his administration, beginning tomorrow with an attempt to override a mayoral veto.

At issue is the balance of power between the executive and legislative branches. Some council members argue that a cooperative spirit that existed during the initial years of home rule has been reduced to a quest for more power on the part of the mayor, who frequently succeeds in upstaging the council.

"Early in the mayor's term, council members were willing to accept the executive branch's evaluation of issues because there was not such a grab for power," said Ward 4's Charlene Drew Jarvis, one of the most outspoken members. "I think the council now feels it has got to remain an equal power."

Although none of the council members will acknowledge it as a motive for their new-found boldness, 1986 is an election year, and that traditionally has been a time for a rigorous examination of mayoral policies, particularly by would-be challengers. During the 1982 mayoral race, four council members ran against Barry. The mayor has not announced his intentions for the 1986 mayoral race.

Jarvis sponsored a bill, later vetoed, that would shift the authority to approve mortgage revenue bonds from the city's Housing Finance Agency to the council. She contends that the agency has failed to respond adequately to the needs of low- and moderate-income residents and to council demands.

Five members of the council's housing committee recommended the override last week, and Jarvis predicts they will get the necessary two-thirds vote, although the mayor is expected to lobby heavily to uphold his veto.

During his two terms in office, Barry has vetoed 16 bills and the council has overridden him four times, according to the legislative services office. In December, the council voted 11 to 1 to override the veto of a bill that would increase the authority of the District's people's counsel.

"The council should use its authority so there is greater respect," said Jarvis. "It should take authority away and abolish boards and commissions and cut the budget if it's necessary. I believe the support will be here to do that. People want to be part of a body that has some guts and uses authority like it knows it has some power."

Jarvis said she will ask for money in the council's budget to allow the Committee on Housing and Economic Development, which she heads, to hire someone to determine whether city dollars are being spent as the council intended.

Ward 2 member John Wilson said he is considering introducing a resolution to establish a council committee to investigate corruption in the city government.

"What we have done," Wison said, "is used the city auditor in place of investigative hearings, and he doesn't have the staff to do all we are asking him to do. It's less heat on the council and the individual council member to do it that way."

At-large member Betty Ann Kane said she agrees that the council should take a hard look at some agencies and place witnesses under oath if necessary.

Each of the council's standing committees has oversight responsibility for a number of city agencies, with authority to abolish as well as create agencies and departments, conduct investigations and hold hearings for which they can issue subpoenas and place witnesses under oath.

But most of the oversight hearings have been routine. The only time subpoenas were issued, according to records, was in 1975, when a committee headed by Willie Hardy ordered police officers to testify about intelligence operations after it was revealed that police had kept files on antiwar and civil rights activists, including Barry and D.C. Del. Walter E. Fauntroy.

Some members say that oversight, rather than legislation, may be the best approach to resolving problems such as crowding in the prison system and rent control.

"People want accountability," said Ward 6 member Nadine P. Winter. "I do believe that people are giving us a mandate and they want us to come up with creative ways to solve problems."

The newest member, Carol Schwartz (R-At Large), who campaigned by accusing the council of being a rubber stamp for the mayor's programs, said, "I think my election sent a loud, strong message that they want strong independent people who would exercise oversight responsibility. The public wants the council to be a watchdog over agencies."

But not all members agree that there is need for major changes.

Polly Shackleton (D-Ward 3) and Hilda Mason (Statehood-At Large) say that the council does an adequate job in obtaining information about the workings of city agencies.

"If there is a perceptible need for it, we do oversight," said Shackleton, chairman of the Committee on Human Services. "We meet regularly with department people and review problems with them. We are able to keep track of a lot of things that go on."

Mason, who chairs the education committee, said she could not think of a committee that has not "carried out extensive briefings." She said her committee will be looking more closely at the operations of the University of the District of Columbia. "But that doesn't mean we will be doing any investigation or witch hunting or anything like that."

"The council could and should do more oversight," said John Ray (D-At Large). "But I would hate to see the council grabbing a theme and running out shouting, 'Oversight, oversight.' "