Amid the public soul-searching and poll-taking that so far has preceded the race for mayor in the District, one political figure remains distinct for keeping her profile below desk-level.

This politician has not (a) challenged all comers to duke it out with her, as has the city's two-fisted Mayor Marion Barry; (b) burst out in anguish over her poor chances of beating Barry, in the manner of fellow council member John A. Wilson (D-Ward 2); or (c) let the word go forth that she was "actively considering" a challenge of Barry only to bow out like council Chairman David A. Clarke. Instead, council member Charlene Drew Jarvis (D-Ward 4) has been stewing.

The influential chairwoman of the council's Housing and Economic Development Committee said she and Barry are locked in a "power struggle" and that for every raid she makes into his turf, he counterattacks.

"The mayor has learned how to play the political game," she said in a recent interview. "From my perspective, so have I. The mayor and I checkmate each other on a lot of things. There is not such an imbalance of power that the mayor can relax."

Jarvis, a possible combatant in either the mayoral or council chairman's race this year, appears to be waiting for the mayor to make a peace offering. If he does, she hints, she may not run against him. If he doesn't, well, Jarvis leaves the question unanswered.

Exactly what it is that Jarvis wants from Barry remains something of a mystery. She alludes to the mayor's "grab bag of goodies" but quickly asserts that she is not seeking favors in exchange for remaining out of the mayoral contest.

Instead, Jarvis says that she and the mayor must come to a "meeting of the minds" and adds, "Certainly I would expect stronger support for my efforts as chairman of the Housing and Economic Development Committee."

Seemingly bitter about Barry's hardball politics, Jarvis cites "four years of undermining and undercutting" as well as his "a lack of recognition" for her efforts to boost economic development and jobs in the city.

Clues to the sour relations between the two can be seen in at least three key issues that recently found them at odds.

Jarvis and Barry clashed recently on the interstate banking bill, a measure vetoed by the mayor and then overridden by the council. The issue then was whether and when large money center corporations could do business here and who would have the power to appoint a regulatory officer for banks in the District. Later, a compromise drafted by Jarvis was approved by the legislative body and signed by Barry.

Second, Jarvis engineered the changed status of the D.C. Housing Finance Agency in early 1985, stripping it of ultimate approval power over bond issues and transferring that authority to the City Council, a move that is known to have irked Barry.

Finally, Jarvis blames Barry directly for a continuing audit of her 1984 campaign finances. Keith Vance, director of the Office of Campaign Finance, has raised questions about late filings and alleged incomplete accounting of contributions. Jarvis says the inquiry is politically motivated and masterminded by Barry, an assertion that a spokesman for Vance denies.

For Jarvis, the lingering questions about campaign finances represent a sure-fire issue that Barry could use against her if she challenged him. Whether for this reason or some other, she acknowledged that a run against the mayor would have to be short but sweet.

"You know when you go into a campaign against the most powerful person in the city, you can expect anything," she said, adding that one possible strategy would be to enter late and limit the mayor's opportunity to attack her.

"Just as you don't want to get yourself in the line of fire for a long period, you don't want your supporters to be exposed also," she said.

Is the mayor worried? In fact, his level of concern about a Jarvis candidacy is hard to gauge. Her popularity was carefully assessed in a poll, widely believed to have been commissioned by the mayor, that was taken within the last month. Barry doesn't acknowledge taking the poll, however, and no results are available.

It is also noteworthy that, while the mayor repeatedly invited Clarke and Wilson to take him on, smacking his lips like a wolf eyeing prey, he did not make a similar invitation to the formidable Jarvis.

Jarvis challenged Barry in the 1982 Democratic primary and made a modest showing. This year, her decision on whether to run again for mayor may boil down to whether she expects or can stomach more combat with Barry as a council member.

It is interesting to recall that Clarke's decision to run for chairman four years ago was linked to his clash with the chairman at the time, Arrington Dixon, and that Clarke, faced with the prospect of Dixon's continuing hostility, risked everything to beat his nemesis.

Jarvis says there comes a time in a politician's career when it is a matter of going "up or out." Her "power struggle" with the mayor may have taken her to that point.