Mayor Marion Barry's gloomy assessment of the limits to what his administration can do to reduce unemployment didn't go down very well among some of Barry's staunchest supporters who recall his stirring campaign promises to help the jobless.

Barry, who used to talk a lot about his dream of putting to work every D.C. resident who wanted a job, said last week his policies at best will put "a small dent" in the District's 10.4 percent unemployment rate.

In the somber tones of a chief executive struggling to avert a deficit this year, Barry insisted at a news conference that it was up to the federal government to deal with the bulk of the unemployment problem.

Council member H.R. Crawford (D-Ward 7) seemed particularly upset by Barry's pronouncement because it offered little hope to the thousands of unemployed and increasingly restive black youths in Crawford's Southeast Washington ward.

"We're not doing as much as we should, and I'm positive we're not doing as much as we could," Crawford said.

Crawford complained the mayor has yet to devise a comprehensive plan to make the most of federal programs and the city's own limited funds. He and other members of the council also were miffed when Barry cut $1 million from the funds budgeted this year to offer job training to high-school-age residents and adults with dependents.

Bernard Demczuk, one of the mayor's strongest supporters from organized labor during the 1982 mayoral campaign, has begun to mutter publicly about Barry's cut in spending for year-round job training and placement.

Demczuk, a former guard at the D.C. jail who is now a chief lobbyist for the local offices of the American Federation of Government Employees, believes there is a direct correlation between the city's lagging efforts to create jobs and the mushrooming population of the city's jail and prison facilities.

"Every single person from the inmates to the department director said jobs is the key. People go to jail because they don't have any money. They don't have any money because they don't have any jobs," Demczuk said.

Barry's "don't-look-at-me" attitude is in sharp contract to candidate Barry's upbeat campaign assessement last year that the city was on the offensive against unemployment. It also signals a subtle shift in the mayor's overall approach to the unemployment problem.

Until now, Barry has avidly subscribed to the notion that local government could combat unemployment by using some of its own limited resources to supplement federal job training and placement programs. Throughout his 4 1/2 years in office, Barry gradually has increased the amount of local tax dollars set aside for jobs program.

But more recently, the mayor seems to be downplaying the importance of job training program and stressing the importance of offering incentives to private businesses to expand or relocate in the District.

The city's new deputy mayor for economic development has spent the lion's share of his time negotiating with developers interested in downtown development. But the office buildings and commercial projects under consideration offer long-term benefits to the city, they would provide little immediate relief to the city's unemployed.

Barry emphasized the importance of economic development at his news conference but insisted it hasn't come at the expense of job training.

"I will never be satisfied . . . until every person in this city who wants to work, who wants job training, is able to get it," Barrry said. ". . . But obviously I cannot do that by myself and the D.C. government cannot do it by itself. People are just not willing to pay the extra taxes."

A City Council committee hearing last week brought out a long simmering dispute between the Public Service Commission and the Office of the Peoples' Counsel on how the city should monitor the city's billion-dollar utility industry.

The core issue is how much independence the peoples' counsel Brian Lederer should have in challenging rate cases brought by the utility companies before the PSC.

Council member Betty Ann Kane (D-At Large), who heads the committee on public utilities, has proposed a bill to give the peoples' counsel more independent authority--a bill expected to get vigorous oppositon from the utilities and the PSC.

The outcome of the legislative battle could have broad effects on utility rate cases, Lederer contends, arguing that if the PSC can continue to define the scope of his office's investigations, then his office "effectively will be gutted."

The three-member PSC over the years has questioned the expenses and methods of Lederer's office. Lederer accuses the PSC of having a too-cozy relationship with the utility companies it is supposed to regulate.