Largely lost in the furor over the city's gambling operations last week was Mayor Marion Barry's proposal to the City Council to balance next year's city operating budget without increasing property tax rates.

The mayor, in effect, told the council District property owners already have been taxed to the limit and he couldn't justify raising the rates any higher, despite the fact that property assessments, used in computing taxes, stagnated or declined last year.

"I cannot ask the citizens and businesses of the District of Columbia to bear more than their fair share of the tax burden," Barry said in his letter.

The mayor's rhetoric was politically impeccable, and his tax proposal is expected to sail through the council. However, some observers have begun to worry that the mayor might be placing the D.C. government in a revenue straightjacket at the same time that Congress has begun chipping away at some of the city's revenue assumptions for the coming year.

"It looks good, but everything that looks good isn't good," said council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee and frequent critic of the mayor's revenue forecasts. "The mayor's proposal will eventually lead us into a deficit situation."

The mayor has proposed retaining the District's current tax rate per $100 of assessed value at $1.22 for owner-occupied residential property, $1.54 for apartment buildings and $2.13 for commercial property.

Barry's plan actually would result in a net loss to the D.C. government of about $5.7 million because leaving the tax rates unchanged would not take into account the increase in the Washington-area cost of living and, thus, the increase in the cost of running the city government.

However, the mayor said he is counting on an unexpected increase in projected revenues from user fees, retail sales taxes and inheritance taxes to cope with that problem.

But at the same time the mayor was unveiling his cheery news for property owners, the District's overseers on Capitol Hill were fomenting problems potentially far more difficult in balancing the $1.9 billion operating budget for fiscal 1984.

In approving that budget last week, the House Appropriations subcommittee on the District penciled in changes that would force the city either to scrounge up an additional $25 million in revenue or cut that amount from the city's already hard-pressed programs.

The subcommittee ordered the District to find an additional $15 million in the budget to help retire the city's accumualated debt. The panel also told the city not to assume, as it had, that it will be able to shift the entire cost of street lighting costs to Potomac Electric Power Co. customers next year.

Betsy Reveal, the city's budget director, insists the subcommittee's action does not pose insurmountable problems.

"To the extent we have to reevaluate certain things, we will," Reveal said this week. "I'm still very comfortable with the budget level requested for fiscal 1984. We think we can live within it."

But Wilson is far from sure the city can balance the budget without making even deeper cuts in programs than Barry already has ordered to try to balance this year's budget.

"All of the public housing in my district is in horrible condition, simply because we don't have any money for it," Wilson said. "The schools will begin to feel it cuts next year. The Department of Recreation already is feeling it. And we're having a tough time getting streets and alleys cleaned in our district."

Wilson, whose committee will consider the mayor's tax proposal this week, said the mayor would have been well advised to have recommended at least a slight increase in the tax rate, to offset the effects of inflation.

But don't count on a groundswell of support for a tax rate increase among council members, all of whom have a healthy instinct for political survival.

"Our tax base is so limited, and I understand people don't want to pay any more money in taxes," Wilson said. "There's a tremendous pressure not to do anything. . . . It's a good short-term political solution."