One sure way to make a major Democratic politician in the District of Columbia squirm these days is to ask, "Who are you supporting for president? Teddy Kennedy or Jimmy Carter?"

Mayor Marion Barry chose his words carefully when he was asked. "The only person who's running is Carter," Barry said. "That means I'm going to support the president if there's no alternative. I don't see one now."

Robert B. Washington Jr., the D.C. Democratic State chairman, is actively supporting Carter, and helped organize a $500-a-plate fund-raiser for the president earlier this year. Washington has a different way of dodging the tougher question.

"The Kennedy name is well known and he could be strong in the District of Columbia," he allowed the other day. Does that mean Kennedy would win, he was asked. "I never reach that point," Washington responded, "because I don't believe Kennedy is going to challenge the president."

Aw, come on, Bob.

Sen. Edward M. Kennedy is all but officially in the race. And there are probably enough Abraham, Martin and John (Lincoln, King and Kennedy, respectively) memorabilia in houses throughout the city to suggest that in this overwhelmingly black city, sentiment for the Kennedy name still runs strong.

This is giving many Democrats in this town late night headaches, even though the District's May 6 presidential primary is months away.

On the one hand, no one wants to offend President Carter, who has been kind to the city during his first 2 1/2 years in office. Furthermore, the White House still wields considerable influence in District budgetary matters.

On the other hand, all politicians want to be welcomed aboard a train that is almost certainly bound for victory. The Kennedy Express is no exception.

No Carter committee has been formed in the District. But there are two Kennedy groups -- the D.C. Committee for a Democratic Alternative and the D.C. Kennedy for President Committee -- both of which are being run by political welterweights.

Third Ward Democratic Club Chairman Mary Ann Keeffe and Fourth Ward Democratic Club Chairman Barry Campbell are co-chairmen of the former. Mark Plotkin, chairman of the Parkview Tenants Association in Glover Park, heads the latter. Neither group can boast of the endorsement of a single major elected city official.

That has not stopped either group from beginning to organize workers and raise funds for their cause. The alternative committee has a coming-out party scheduled for next week. The Kennedy committee is already passing out red-and-white "D.C. for Kennedy" bumper stickers, and has a fund-raiser scheduled for then as well.

If and when Kennedy declares, the District's political leaders are expected to begin choosing up sides quickly. In the process, they will probably replace the Plotkins, Campbells and Keeffes of the world.

Kennedy is expected to announce a decision on his candidacy by the end of the year. The first local skirmishes will begin in February, when D.C. Democrats caucus throughout the city to choose nominees for 13 delegates to the party's nominating convention. The remaining six delegates will be chosen later by either those already elected or by the D.C. Democratic State Committee.

Few city politicians seem worried that their lack of early support for Kennedy may result in them playing a subordinate role to the current Kennedy committee heads.

"Whatever advantage there is to being early has long since been lost and most people don't think it imperative to do so," one leading city Democrat said. "And the senator recognizes the need to establish rapport with the established powers if he does decide to run."

Bob Washington said he is convinced that Carter will carry the day. "When it really comes down to it," Washington said, "the president's record in Washington is one of strong accomplishments. When it really gets to short straws, people will examine his record rather than (vote on) emotion and charisma."

That's the same kind of thing Bob Washington was saying last year when he was masterminding Sterling Tucker's campaign for mayor . Tucker lost.

Come on, Bob. Get serious, man.

In the 1976 Democratic primary, Carter handed a serious blow to local party leaders hoping to be power brokers at the convention by defeating two slates of uncommitted delegates -- one headed by Del. Walter E. Fauntroy and the other by then-Mayor Walter E. Washington.

As a result of that, many city Democratic leaders are now contending that uncommitted slates -- which Fauntroy for several years used as a way of trying to broker the city's votes at Democratic meetings to the chagrin of some of his one-time allies -- are a thing of the past.

"If you're not committed, you don't stand much of a chance of getting elected," one leading city Democrat said last week. "People in the District waited too long for the opportunity to vote up or down for president to blow their vote on someone who wants to cast it at a convention later on."

If for some reason the city's Democratic leaders decide to go uncommitted, the lower echelon Kennedy supporters could win places in the delegation as beneficiaries of strong Kennedy sentiment.

The May 6 election will also decide who gets the Democratic nomination for the city's non-voting delegate seat in Congress, and City Council member John A. Wilson (D-Ward 2) appears to be intensfying his test for a possible challenge to Fauntroy. It would be the first serious challange to Fauntroy since Fauntroy was elected in 1971.

Wilson is telling acquaintances that he has lined up several hundred thousand dollars in campaign fund pledges. A poll is being taken to determine how Wilson would do in a race against Fauntroy, according to some of Wilson's friends. If Wilson runs against Fauntroy next year, sources said, it will be without the blessings of Mayor Barry, who would rather see Wilson run for reelection in 1980 and challenge Arrington Dixon for council chairman in 1982. (Barry might then support council member John Ray for Congress).

But Wilson doesn't want to wait that long and has no guarantees that Barry may not find someone else in 1982, the sources said.

City election law provides Wilson with the best of both worlds because the primary election for Fauntroy's seat will be held in May and the primary for Wilson's Council seat in September. If Wilson runs against Fauntroy and loses, he could still seek nomination for reelection, win another term and be around in 1982 to run for whatever he wants.