D.C. City Council member Betty Ann Kane, a Democrat who is running unopposed for her at-large seat in the Nov. 2 general election, has been considered a gadfly of sorts throughout her political career.

The tall, rangy, 41-year-old woman with a keen eye for detail and a burning political ambition, is better known for her stinging barbs and criticism of the work of her colleagues and the mayor than for her prowess as a legislator.

"Her greatest contribution has not been in the sense of introducing bills, but in her intelligence and analytical capabilities and quickness," said one veteran council member. "She's not a team player."

Sensitive to the criticism and chastened by an abortive bid for the Democratic mayoral nomination that left her $32,000 in debt, Kane now appears to be trying to mend fences and improve her standing on the council. She still wants to be mayor, and plans to try again in four years. But she intends to lay a foundation first.

A long-standing feud with lame-duck Chairman Arrington L. Dixon cost her a committee chairmanship -- a position that might have enhanced her stature as a mayoral candidate. She doesn't want to make a similar mistake by alienating council member David A. Clarke (D-Ward 1), who defeated Dixon in the primary and faces token opposition for chairman in the general election.

"People didn't elect me to go there and play along," Kane said last week. "People wanted me to speak out -- to be the lone voice when it was needed."

But she added that "being a [committee] chairman gives you a different position, vis-a-vis your colleagues, because then you've got something to bargain with."

Kane has had "heart-to-heart" talks with several council members in recent weeks, according to a knowledgeable source, in which she has lobbied for support to become chairman of the Judiciary Committee, which Clarke would vacate on becoming council chairman next January.

Clarke criticized Dixon during the primary for having wasted Kane's talents, bypassing her for a committee chairmanship despite her seniority. But Clarke declined to say last week whether he will pick Kane for a chairmanship as part of the reorganization plan he would submit to the City Council Jan. 3.

"I said I'd try to find a role for everybody, but I did not commit myself during the campaign to give any particular person a particular assignment," Clarke said.

Other members who covet the assignment include John Ray (D-At large) and Wilhelmina J. Rolark (D-Ward 8), both of whom are lawyers, and Nadine P. Winter (D-Ward 6). Neither Winter nor Kane is a lawyer.

Nonetheless, Kane already has begun to prepare a list of issues for the Judiciary Committee to tackle. High on that list is a review of the long-range budget implications of the new mandatory sentencing law approved by voters in September, as well as consideration of alternatives to imprisoning persons convicted of nonviolent crimes.

"There was an overwhelming message [from the mandatory-sentencing initiative] that people are fed up with the current judiciary system," Kane said. If she doesn't get the Judiciary assignment, Kanes said she intends to devote most of her time to seeking ways to reduce unemployment.

Kane, a New Jersey native, is a Phi Beta Kappa graduate of Middlebury College in Vermont with a Master of Arts degree from Yale University. She got her first taste of politics in Connecticut while at Yale and remained active after she and her husband Noel, a lawyer, moved to Washington.

Kane was an assistant professor at Catholic University and director of public programs at the Folger Shakespeare Library before she was elected to the D.C. school board in 1974.

She won an at-large seat on the City Council in 1978 and appeared to be launching a promising political career. But her ambition to become mayor came close to leading her to political ruin earlier this year.

With her term on the council due to expire at the end of the year, Kane announced in February that she was a candidate for mayor--a long-shot prospect, especially for a white candidate in a city that is more than 70 percent black. Kane told her supporters that she was "sick and tired" of the inefficiencies of Barry's administration, and expressed confidence that she could topple the mayor.

But the subsequent entry into the race of Patricia Roberts Harris, a former Carter administration official with high name recognition, dashed the chances of Kane and three other council members running for mayor -- John A. Wilson (D-Ward 2), Charlene Drew Jarvis (D-Ward 4) and Ray.

By mid-June, Kane's campaign was badly in debt (she used $16,000 of her own savings to keep it afloat) and she was briefly faced with the prospect of being forced out of politics. As she recalled later, the thought of leaving her $41,000-a-year council job at the end of the year was "chilling."

"It would be very frustrating to be on the outside -- seeing things were not right and not being able to try do do something about it," Kane said.

She averted the disaster by pulling out of the mayor's race on June 21 and immediately launching a reelection campaign for her council seat. She crushed two opponents in the Sept. 14 primary, receiving 55 percent of the total vote and carrying seven of the city's eight wards. She lost only in Ward 8 in Southeast Washington.

Kane said that her strong citywide showing may have helped minimize the political damage caused by her disappointing performance in the mayor's race. She believes she may be in a better position to run again for mayor than Jarvis or Ray, who stayed in the race this year and received only 3 percent of the primary vote each.

"I don't see any of the people on the council now as rivals," she said.