The notion of Jesse Jackson as mayor of Washington, D.C., an idea he floated just over a week ago, continues to gain altitude. Politics-watchers from columnist David Broder to the editorial board of the New York Times have weighed in over the past few days with ``Run, Jesse, run.''

Ron Brown, new chairman of the Democratic National Committee and former chairman of the Rev. Mr. Jackson's presidential campaign, does not give out his own advice - not exactly. But, he says, ``a lot of people are expressing the view that it would be good for Jesse Jackson, good for the city, good for the party.''

Mr. Brown has yet to encounter a Democrat who dislikes the idea, he says.

That may not include current Mayor Marion Barry. Jackson says he would not run if his old friend, Mr. Barry, were in the race. And despite his beleaguered reputation, Barry shows every sign of running again.

If Jackson were elected mayor, he would almost certainly be out of the presidential sweepstakes in 1992. But he would also fill a gap in his r'esum'e; he has never held elective office.

Brown says he thinks Jackson could also do something for the city. ``We've got a real problem with youth in this city,'' he notes. ``There's no one around who can do more to energize and motivate youth.''

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