The aide said that Madam Secretary laughed at the very idea. Patricia Roberts Harris, secretary of Housing and Urban Development, running for mayor of the District of Columbia in 1982?

"No way," said an amused acquaintance of Harris', with a hearty chuckle. "Being mayor is worse than being secretary of HUD."

Another bewildered friend of the tough and high-mannered secretary added, "She herself allows for the fact that that's not her shtick. She's just not the press-the-flesh type. Besides, I don't think anybody is going to be able to just come out of the blue without being involved in grass-roots political efforts and pull it off."

Already, at least one informal meeting has been held to explore the Harris candidacy, sources said. Harris said Monday that that's news to her.

Three years is a long way off and Harris may change her mind. The clear message, nevertheless, is that behind the sometimes thin veil of Democratic unity, the city's perennial politicians have already begun choosing up sides for the next campagin.

There's nothing sinister about that. It's par for the course in big city politics.

Whether she wants the job or not, Harris is in many respects a logical person to unify two major blocs in the local Democratic party that lost when Barry won - those who backed former Mayor Walter E. Washington and those who supported Sterling Tucker, the former chairman of the City Council.

"She would bring together that Walter Washington crowd, that Tucker crowd, and she would also run well west of Rock Creek Park," said one knowledgeable city observer.

Like Washington, Harris is a Howard University graduate of the World War II era. She is an established black middle-class woman, a lawyer with one of the old-line professional degrees that many established black Washingtonians respect - even though she was born in Mattoon, Ill.

Harris has the polish, social graces and crisp diction that does not embarrass many of those who support Sterling Tucker. Her civil rights background is as a moderate. And she was a friend of Tucker in his worst political hour. Right after Tucker lost the Democratic primary, it was Harris who quickly offered him a job on her staff. Tucker is now assistant secretary for fair housing and equal opportunity.

But there are also some drawbacks. Harris has a limited record of activity in local political affairs. And for those who consider age in political candidacies, Harris will be 58 on May 31, 1982, and perhaps a bit old and a bit staid for some of the younger liberals whose clout appears to be increasing in city politics (Barry will be 45).

One of the major goals of Marion Barry's political strategy over the next 3 1/2 years seems to be to broaden the narrow base that gave him a slim-margin of victory in last year's crucial and close three-way Democratic primary.

Those talking it up for Harris seem bent on keeping that base slim. "It's not like the liberals looking for an alternative to Carter. Marion is too new and he's done a generally progressive job," one past Barry rival said. "But by the end of this year, around Christmas time, something will begin to jell. People will begin looking around for someone to oppose him in '82."

City Council member John A. Wilson (D-Ward 2) may not be as frustrated with elective politics as suggested this week when he stormed off the City Council dais and threatened to resign.

The 35-year-old, sometimes erratic city legislator is volunteering these days that he is considering opposing Del. Walter E. Fauntroy in 1980 or 1982.

The talk of a possible Wilson candidacy probably says as much about Wilson as it does about Fauntroy - who was once the undisputed kingpin of local politics and the veritable godfather of aspiring city politicians.

In recent months, Fauntroy's political strength had been seriously cast into doubt by his handling of the faltering drive for congressional voting rights and his ill-fated support of Sterling Tucker's candidacy for the Democratic nomination for mayor. And many of those who once staffed his political organization - Wilson helped run Fauntroy's first campaign - are lining up against him with goals of their own.

Many are not surprised to see that for the first time a major established politician is talking about taking on Fauntroy. "Someone's going to run against Walter because of this split among Walter's people," said one leading city Democrat, noting that both Tucker and Barry had at one time been close to Fauntroy. "Whenever you split folks and you split people, you leave yourself wide open."

One friend said Wilson has always wanted to be in Congress, and conditions in his own ward may be encouraging his quest for greener political pastures.

Many of the elderly persons and young liberals who were essential to Wilson's political base are being forced out of the ward by housing restorations and condominium conversions, some ward observers said.

Still, running against Fauntroy in 1980 would be a do-or-die proposition for Wilson. In order to do it, Wilson would have to bow out of the race for reelection to his council seat. On the other hand, by waiting until 1982, Wilson could allow Fauntroy to be dragged down more by what some see as a slumping and inevitably doomed voting rights drive under Fauntroy's leadership. If Wilson lost then, he would still have a council seat, providing he won reelection in 1980.

In the meantime, one council member suggested, Wilson - who once mumbled about running for mayor last year and then mumbled about running for City Council chairman - has nothing to lose by mumbling, or letting it be mumbled, that he is interested in knocking off Fauntroy.

"John knows that rumors that you are the chosen person to run against Goliath makes it appear as if you are David," the colleague said. "There's no harm done to him."