City Administrator Elijah B. Rogers has an unusual way of dealing with skeptics of Mayor Marion Barry's financial policies. Borrowing a page from the Allstate Insurance commercials, Rogers simply cups his hands, smiles broadly, and says, "Trust us." The city is in good hands with Barry.

Rogers' technique may be useful in selling life insurance policies, but it has done little to quell the chorus of skepticism from the D.C. City Council since Barry released his 1983 budget proposal.

The release of the budget coincides with the start of the 1982 mayoral campaign, which may partially explain the intensity with which some of the council members have vented their displeasure.

After all, four council members are pondering challenges to the mayor in the Democratic primary in September, and Barry's handling of city finances looms as a key issue.

Yet the deluge of bitter criticism seems to transcend the bounds of political sport that usually attends the release of an election-year budget. And, rightly or wrongly, it seriously calls into question the credibility of the mayor--the city's chief spokesman and negotiator. As far as these council members are concerned, there are pretty big gaps between Elijah Rogers' fingers.

Clearly, the council members have wasted little time in defining the overriding budget issues. But there are gaps between those fingers as well. The careful thing to watch during the next two months is which council members--if any--will offer realistic alternatives to Barry's proposals.

At the heart of the Council's criticism is a basic distrust of the tax revenue estimates and other numbers Barry used in projecting a balanced budget. Council members have complained that the estimates are too optimisitic for these tough economic times.

Even more galling to some of the mayor's detractors, including council members John A. Wilson (D-Ward 2) and Betty Ann Kane (D-At-Large), is that Barry is taking bows for balancing budgets that they claim aren't truly balanced.

The current fiscal 1982 budget, for instance, is said to be "balanced" by the mayor. And yet it doesn't contain sufficient funds for new salaries being negotiated or for new programs recently approved to offset cuts in federal aid for working-poor families.

Just how much more the mayor will need in supplemental authority or where that money will come from are questions yet to be fully answered. Rogers has taken to extending his cupped hands whenever that subject comes up.

Barry's 1983 budget poses a few riddles as well. For instance, what makes the mayor think President Reagan and Congress will be in the mood to increase the federal payment to the city from $336 million this year (a record high) to $361 million next year?

Barry is counting on a $25-million increase in the payment to cover an anticipated rise in employe salaries, an increase in the city's contribution to the employe pension fund and additional Medicaid costs.

But if Congress doesn't cough up the extra dough, where will the money come from? Again, answers are hard to come by. Cup those hands one more time.

There are other complaints as well. Barry was blistered by some for reneging on his commitment to start retiring the so-called "noncash" half of the city's $388-million accumulated debt. He promised to set aside $10 million a year for that purpose, but recently decided to use that money instead to increase funding for the D.C. school system next year.

Wilson, who is chairman of the council's Finance and Revenue Committee, wrote off Barry's new budget as a "master political document" that would lead unsuspecting D.C. citizens further down the road of excessive government spending and taxes. Nothing short of a complete overhaul of the mayor's budget would suffice, according to Wilson.

But the sharpest criticism of the mayor came from his erstwhile compatriot, council member John L. Ray (D-At Large), who formally announced his campaign to unseat Barry last weekend.

In his formal remarks, Ray accused Barry of having resorted to budgetary tricks that enabled him to transform a potentially massive deficit to a $7 million surplus in the fiscal year that ended last Sept. 30.

What's more, at a press conference that followed, Ray suggested that the mayor wasn't even telling the truth about the extent of the accumulated debt.

Such is the depth of distrust of Marion Barry. But so far, there are no alternatives.