A get-tough memo last week ordering new budget austerity in the District government came from Mayor Marion Barry, but its origins may be traced to the growing clout of the D.C. Council in shaping the city's financial affairs.

The memo acknowledges "council-initiated tax cuts" that have curtailed a steady growth in city revenue that has been the foundation of Barry's expansionist government spending policies, council aides said, and have taken some of the fat out of the city's $2.6 billion operating budget.

The council twice this year rejected efforts by Barry to take advantage of federal income tax changes to increase city income taxes. The council pared several areas of city spending -- including, for example, $11 million in new personnel costs -- before approving the city's 1988 operating budget.

Last year, over Barry's initial objections, the council approved higher homestead property tax exemptions, voted additional property tax relief for senior citizens and eliminated most of the tax bite from the city's inheritance and estate tax laws.

While the council has been asserting itself, Barry has been confronted as well with rapidly rising costs of public safety, millions of dollars in expected pay increases that are not funded in the budget now, cutbacks in federal funding, rising costs of paying off the city's debts and only moderate revenue growth from the economy.

The net effect has been to wring millions of dollars' worth of flexibility out of the budget and to force Barry to reconsider his once-expansionist spending policies by focusing more on trimming District spending.

"I think we've finally reached the point where the joyride is over," said council member John A. Wilson (D-Ward 2), chairman of the finance and revenue committee and longtime critic of Barry's handling of city budgets. "We've hit the wall."

Wilson hailed the Barry memo, which called for a slowdown in hiring and ordered agency heads to prepare possible cuts of up to 10 percent in the current year's budget, as "the most responsible statement we have had {on the budget} in years."

Wilson has been a leader of council efforts to confront Barry's spending policies. In addition to real concerns about the financial shape of the city, some council members have been anxious to distance themselves from Barry, whose administration is being investigated on several fronts.

On budget issues, Wilson and other leaders of the council have complained for years that the mayor has underestimated true costs of crucial budget items such as corrections and police in order to fund politically popular but costly programs. Funding for police overtime in the current fiscal year, for example, was budgeted for less than the city spent last year even though Barry has acknowledged that overtime costs are continuing to go up.

Barry, they say, has been able to make up the difference each year because revenue invariably exceeds his conservative projections, allowing for midyear budget revisions to cover the costs that had been underestimated in the budget.

Without the increased taxing authority and other revenue adjustments, the additional funds available midway into fiscal 1988 likely will be far smaller than the $60 million amount Barry redistributed at midyear in fiscal 1987. "No more windfalls," said Wilson.

Another major factor in the city's financial picture is labor negotiations under way with unions representing most city employes. There is no money in this year's budget for what could be $60 million in pay increases this year alone.

Richard C. Siegel, Barry's budget director, has been seen as the guiding hand in Barry's new toughness, some administration officials said, along with city controller N. Anthony Calhoun. Siegel is being privately referred to as "Dr. No" by some agency heads.

Siegel wrote Barry's memo and specifically warned against scare tactics by agency heads who in time-honored bureaucratic fashion might target popular programs for cuts so as to bring outcries from the public. Such strategies "are not acceptable," the memo said.

One remedy for the changed circumstances could be a proposal for higher taxes. However, Barry has not made any such suggestion, and Wilson has warned that it would not be warmly received.

Wilson, who along with six other council members faces reelection next year, said he would oppose a tax increase, offering the view that high rates are forcing middle-class residents and businesses out of the city.