D.C. City Council member Betty Ann Kane is the first and only white person electd to an at-large position in the city government. Now she is coveting the mayor's office and finding that even her previous supports have serious doubts whether she should run for the city's top elected job in next year's Democratic primary.

"I've told her that I don't think she should run at this time," said Joseph Carter, D.C.'s alternate Democratic national committeeman who chaired Kane's 1978 council race. "I hope she would not. There's a big difference between running for an at-large seat and running for mayor.

"Would people be willing to accept a woman at this time, and would they be willing to support a white candidate? I didn't even think about that when she ran before," Carter said. "I have no problem with her looking to run for her own seat."

Nonetheless, the 39-year-old Kane, who was elected to the council in 1978, says she is "very seriously considering" running for mayor. She is openly seeking support, armed with a new poll that she said shows Maryor Marion Barry in serious political trouble and her beating Barry in a head-to-head race.

But at this early stage, with no candidates officially announced, a two-way Democratic primary seems unlikely. Barry is considering running for reelection, and the list of potential challengers includes former council chairman Sterling Tucker, current Council Chairman Arrington Dixon, as well as council members John L. Ray (D-At-Large), David A. Clarke (D-Ward 1) and John Wilson (D-Ward 2).

Barry disputed the findings of the poll, saying, "Many experts believe that if you have a poll designed for a candidate, the pollster can produce results that are pleasing to that candidate." He added that polls three or four years ago "showed that Sterling Tucker would be elected mayor."

In what sounded like a slogan for an evenutal 1982 campaign, Barry said, "I produce results, not rhetoric." The mayor challenged Kane or any other potential opponent to compare their record to his own, and he cited housing, jobs and his handling of the city's financial crisis -- without, he said, significant tax increases -- as his three strong suits to bring to a reelection campaign.

Kane, who has been elected city-wide since enetering D.C. politics as a school board candidate ijn 1974, has many of the ingredients of a potentially successful mayoral candidate, even in such a crowded field. She has name recognition, a reputation as a hard worker who knows the issues and a potential base of support from politically active Capitol Hill, where she lives. With a toothy smile permanently affixed to her face and an arsenal of facts and figures at her fingertips, she would be a Madison Avenue advertising agency's dream candidate.

But Kane also has a few handicaps. Her ambition and political shrewdness have made her some political enemies. Some business community leaders and others have called her unpredictable, with a penchant for trying to please all sides and in the process pleasing no one. She faces a reelection race for her council seat next year and would have to give it up to make the mayoral run. Moreover, she is a white politician in a city that is more than 70 percent black.

Moving to Washington 14 years ago with a master's degree in English from Yale, Kane has been on something of a fast track in District of Columbia politics. The council chairmanship or the mayor's seat is the next logical step up.

Any Kane mayoral run would automatically conjure up images -- already prevalent in some sections of the black community -- of a white-backed "master plan" to regain political control of the nation's capital. With many blacks already fearful of whites moving into formerly black neighborhoods like Capitol Hill and Shaw, and with those new "urban pioneers" becoming increasingly active in local politics, subscribers to the conspiracy theory may see a Kane candidacy as fullfilling as prophecy of Barry as the last black mayor.

"If she gets out there and whites start lining up behind her," one Kane opponent predicted gleefully, "that while conspiracy theory will come up. Race will be the issue."

Kane insists that race will not be a factor. She said that "politicians are more hung up on that than the voters," and she points with pride to her strong 1978 showing in areas with large black populations.

In that crowded race, with her closest opponent being H. R. Crawford, now that Ward 7 council member Kane put together a solid white voting block and then held her own in the black areas. She won overwhelmingly in Ward 3, the predominantly white and affluent area of the city west of Rock Creek Park, and she won handily in the wards with significant white populations -- Ward 1, which includes Adams-Morgan and Mt. Pleasant, Ward 2, which includes Dupont Circle, and her home, Ward 6, which has most of Capitol Hill.

Aware of the political odds she faces, Kane lately has been spending more time in the black community than west of Rock Creek Park. "She is one of the few elected officials who attends almost every activity," said Calvin W. Rolark, publisher of the Washington Informer and a principal spokesman for black consciousness in the nation's capital.

One 1978 Kane supporter, Ted Gay, now chairman of the D.C. Democratic State Committee, said "I would support her if she decided to run at-large. It's fair to say that people have been impressed with Betty since she won her at-large seat . But these comments are attributed to her in her current position. I could not support her for mayor."

The mother of two children in D.C. public schools, Kane is a rail-thin, 6-foot tall woman who speaks softly. But still she is forceful, articulating every syllable like the English teacher she once was. To her critics, however, some of her speeches at council meetings take on a preachy, holier-than-thou air.

Her self-confidence, such as when she talks about how she thinks she can win the mayor's seat next year, bordersk on arrogance to some of her critics. To others, she is a shrewd and tough rival for power on a council full of members with considerable egos.

She and her small staff use their time to pick and choose their issues and decide where to take their stands. As with the recent estate tax issue, she often ends up isolated on the council. Kane works through the thicket of D.C. government bureaucracy to find new statistics to feed into her arsenal of facts, often leaving her colleagues jealously accusing her of being the beneficiary of a white network of career government employees and political appointees.

Kane says that she simply takes the initiative to seek out information. "I make a real effort to get the facts where other people may sit back and wait for the facts to come to them," she says.

She came on the council as a lone crusader against the council's frequent use of its emergency powers. She supports a citizen's referendum on the Washington Convention Center even though the facility is well under construction. She has sponsored a mandatory no-fault automobile insurance measure. And she has been a consistent thorn in Barry's side, mostly on financial issues, where she criticizes the mayor's handling of the current fiscal crisis.

Kane said that her constituency is "broad-based," but that it's still too early to start targeting specific groups. She gets high marks from the limited-growth advocates of Capitol Hill and Georgetown, and she has supporters in the business community, especially among realtors, who note that she voted against a bill to limit condominium conversions. "She has probably exhibited more intestinal fortitude than many on that council," said developer Michael Brenneman.

Kane thinks she can do a better job than Barry as mayor, which is why she says she wants to oust him. "The people want an alternative," Kane said recently. "One of my priorities now is to get some common sense focused on the financial matter."

She is buoyed by the findings of her poll, commissioned for about $7,000 through private donations she declined to disclose. The poll was conducted during the first two weeks of May by Cambridge Survey Research, the polling group headed by former White House pollster Patrick Caddell.

According to Paul Maslin, one of the firm's pollsters, the survey of 450 representatives voters found Barry with a 47 percent favorable rating and a 45 percent unfavorable rating. That thermometer of personal feelings put Barry lower in voter sentiment than any of the other potential candidates, Maslin said.

In response to a pool statement that said "Marion Barry has shown he can't handle the job. We'd be better off trying a new mayor," 53 percent agreed and 35 percent disagreed, Maslin said.

Coupled with those findings, Maslin said the poll found Kane with an 8-to-1 favorable/unfavorable rating. He said the poll also found Kane narrowly beating Barry among the poll's respondents, 41 to 38, in a two-way race. Masline said he did not want to reveal the numbers in the more crowded field, since they did not scientifically reveal anything significant. "No one had any sort of significant lead," he said. "They were all just sort of bunched."

Kane said she does not expect an "Anybody But Kane" movement if she runs, and that at any rate, such an effort would backfire and create a sympathy backlash for her. "The city is very positive," she said. "I've found in all of my previous campaigns that race is not an obstacle."