Is Marion Barry really the upopular and inadequate mayor his image in the newspapers and on television would sometimes lead you to believe? Or is he a man fighting to the limits of his powers, as he sees it, to deal with city troubles stored up from long ago and only uncovered, not created, by his administration?

Perhaps his televised address tonight will give some clues, for it is hard to tell. Judging a Distict mayor is difficult because he has only so much power. After all, this city is run for and by the federal government. It is still the nation's capital before it is anyone's home town. To see "the men in charge" here, you have to go the White House end of Pennsylvania Avenue or the Capitol Hill end. Any stop in the middle of the Avenue, at the District Building, will only get you middle management: a mayor and city officials who oversee the city's day-to-day operation, making policy and budget recommendations but no final decisions.

So who is to blame for the city's untended problems -- the federal government or the mayor?

To get an answer, you have to judge whether the current city government is doing all within its power to serve the people who live here. The press and television news don't always answer that question. Stories abound about Marion Barry's arrogant style -- taking a deal from a local bank on a mortage, telling demonstrators to "go to hell" and getting rid of all city limosines but his own. But those stories don't tell you if his government is doing as good a job as it could.

The hidden truth may be that it is not. Despite shouts about anonymous congressmen controlling the city -- the federal government has always been a good scrapegoat -- the reality is that Marion Barry as District mayor does command one great power: the power of vision. The vision could be to provide more low-cost rental housing, to get more industry with jobs for blue-collar workers and to improve the schools so they can help the large population of poor people end their dependence on public welfare.

If Barry had such a vision -- or any other -- for this city's future, then he could make every part of that vision aa priority for his government's day-to-day operation and make it a reality. A solution to the budget problem would become part of that vision. But now the budget crisis is a problem apart from everything; everyone knows it is out there, but instead of joining forces, everyone is fighting alone to make sure his program or job is not cut . f

The absence of a vision on Barry's part of where the city is heading makes it difficult for residents to work together with any sense of purpose. Businessmen attack the mayor and his tax package while clergymen ask if he is up to handling the job. Suddenly, one man, Marion Barry, becomes the issue. uAnd meanwhile, Barry's energy is consumed in pointing fingers at anonymous, mostly white congressmen whom, he blames for this mostly black city's problems. mThere are also fights with the press. He seems to feel personally attacked by the press that, with rave reviews for him in the past, has been so key to his political success.

"The thing with the press," he says with an air of exasperation. "I don't know what impact the press has on people. I'm not taking any polls. I'm not running for office. All I'm trying to do is make sure that the people who really supported me in the primaries don't get disaffected. I've seen no organized disaffection from them. They've got some questions like anyone else, but as far as that hard core goes, I've got no major problem.

And who are the supporters that the mayor call his "hard core," the people he doesn't want to lose at any cost?

"I'll tell you who supported me: the people in Ward 3, the labor unions, police, fire fighters and teachers, the gays, and 30 percent of the black voters. I lost Ward 8 where all the black people live. They didn't support me."

The mayor leans back in his chiar as he considers the question of how his government is doing after a year and a half. His own answer is best seen in his approach to the budget. He has gone to the Greater Washington Board of Trade, to Congress, to the newspapers and to community groups to explain why he has had problems with the city budget. At those meetings Barry -- the young black mayor -- is accompanied by conservative, mostly white accourntants who give him support with nods of agreement when he says the budget problem is not all his making and he does not have the power under the home-rule charter to solve the problem.

For instance, he says he can't fire the large number of bureaucrats in the city government -- the people whom, it has been suggested, he get rid of before he fires jail guards or closes recreation centers. The bureaucrats are protected by the civil service law, Barry says: and even if he were to fire them, the severance pay would negate any savings that come from getting them off the payroll.

Barry dwells on the limits of his power. The federal payment -- the city's largest single tax payment -- is unpredictable, he say, making budget planning difficult. In 1979, the federal government gave the city in payment only four days before the next budget year began.

Barry says he is also limited in control of the city government everyone thinks he heads. He doesn't control the school system, which uses 20 percent of the city budget, and he doesn't controll the courts, the bail agency or the parole board.

He is also limited in his ability to pass taxes. He wants to tax non-residents who work here. He would have collected $299.7 million in taxes, he says, if the district had a commuter tax like most states have.

The tax problem, he goes on, extends to congressional staff and White House appointees who don't have to pay District income taxes. He suspects that some of them pay no taxes and is checking records in other states tgo see if they do. There is also the problem of tax-exempt organizations. "The theory of tax exemption," the mayor says, "is that it is given to groups that offer services to the community in return for not paying taxes. These groups don't do anything for us."

What angers Barry the most is when businessmen try to get around him by going to Congress. He moves forward in his chair and stares hard at an interviewer: "Some people in our business community don't believe in local government. I get reports when they go to Congress. They've been up on the Hill trying to undo my tax package. . .It's my authority to levy taxes. . . .What good is self-government if you are going to undo it?"

If Barry feels he doesn't have full power to do his job, who does he think are the true masters of Washington D.C.?

"The true masters are the masters of the money," Barry says, "the four congressional committees. . . .We don'telect anyone to Congress, but they run the show. I don't vote for Dellums or Leahy.I don't have a vote in California or Vermont."

But if Barry has his way, Congress will not get off lightly as the mayor proposes a cure for the city's finanacial ills. Barry says he has "heavy ticket items" for the federal government in his plans -- to be disclosed in his speech tonight -- for paying off the city's debts.

Still, with the budget crisis beating down on him and Congress holding the city's purse strings, Barry gives himself high grades for his overall performance as mayor.

His biggest accomplishment, he believes, has been to create an "open" government. He says reporters are angry only because they have "95 percent freedom [in the District building] instead of 100 percent freedom." And he claims that, despite some stubborn bureaucrats, his administration is more responsive to citizen complaints than any city government before him.

Listening to Barry, one feels mixed understanding for his problems and discomfort at the flashes of arrogance in his demeanor. Unlike his predecessor, Marion Barry is clearly the mayor of the District of Columbia. pHe is in charge and is there to be seen. He is superior to any leader this city has had for years. He has named good people to head some city agencies.

But Barry has yet to do what the mayor can do, federal government or no federal government. The mayor can set priorities for the city government; he can outline an order of business to be enacted, of troubles to be dealt with. Washington is tending toward becoming a city of the very rich and the very poor. To manage such a future, the city needs more blue-collar jobs; that means attracting some industry. It needs better schools, too, and it needs more afforable housing -- in particular, decent apartments for low- and moderate-income people -- if it is to avoid awful slums and forever overcrowded public housing. That means encouraging developers to build apartment buildings. And finally, with the limited amount of money left over from the current budget crisis, the city will need a lean, efficient bureaucracy to do the work that the bloated, lazy government in the District Building today is leaving undone.

The mayor can do things to address these problems. But Barry has yet to use his position to set priorities for the city government and then fight the federal government to make sure they get done. He has yet to make a campaign of the city's troubled schools, housing shortage or need for jobs. He has not truly shaken the city's fat bureaucracy and gained improved municipal services for everyone in the city. At best, he seems to be running a government that is properly obsessed with the city's budget problems but is improperly ignoring the city's many other problems.

"I know I'm unpopular in some quarters," Barry says. "But there is no way a mayor could be popular under these conditions. How could [a city worker] who is losing a job feel good about me? That would not be natural. But they shouldn't like Congress or the council, either. I can only do so much."

True, Mr. Mayor, but you could be doing more.