Mayor Marion Barry and a top aide indicated yesterday that they are concerned that the public may not believe that the administration had tried hard enough to cut fat from the city bureaucracy.

Barry and D. C. Budget Director Gladys W. Mack made the remarks at a meeting of all city department heads to "refine" plans for some $26.1 million in budget cutbacks.

The reductions are part of Barry's overall plan to avoid a projected $172.4 million budget deficit for the fiscal year ending Sept. 30.

"One of the concerns we have had is the public impression of the cutbacks we're making," Mack said. "But I'm sure the citizens will be convinced."

The approach was a marked shift from Barry's earlier public statements about the budget crisis, in which he sharply criticized Congress and defied the City Council to come up with a better plan to balance the budget if they did not like this.

Barry said the administration plans to issue a detailed analysis of the effects of the planned reductions. "We're going to demonstrate to the public that this government is tightening its belt," the mayor said. "We've made major reductions."

Barry would not comment when asked about the other two elements of his plan to balance the budget -- a $66 million supplemental request of Congress, and $24 million in increased and new taxes and user fees that he has asked the City Council to approve.

Earlier this month, before audiences like the Greater Washington Board of Trade, Barry hammered at Congress for failing to approve an adequate federal payment for the District of Columbia and stated he would begin wholesale layoffs of city employes if the Council did not approve his tax package.

These elements, which had become part of a standard speech on the budget crisis, were missing from Barry's press conference yesterday and from a talk the mayor gave Tuesday to the local chapter of the Public Relations Society of America.

"With all this talk about inflated payrolls and bloated bureaucracy, the public is wondering whether the cuts are for real," said one adminstration official who asked not to be identified. "They want to be assured before they are willing to talk about tax increases." "

Barry said yesterday that he also is abandoning "time frames," such as a May 1 deadline he previously announced for Council action on the taxes.

The shift in focus comes after a series of developments that threaten to tear Barry's budget-balancing plan apart:

Influential sources on Capitol Hill have indicated that the prospects for approval of the full supplemental appropriation are dim.

Council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee, has announced that there is "no support" for the tax increases on the Council and has said he has no plans to hold hearings on the measures.

Some city department heads, like Department of Corrections Director Delbert Jackson, have said they cannot comply with the budget cuts.

Barry's plan calls for eliminating 1,223 city jobs, 550 of those through actual firings and the rest through attrition.