In handing Democrat Sharon Pratt Dixon a victory of astonishing proportions in Tuesday's mayoral election, voters issued an undisputed mandate for change in District government. But in exit interviews, they sent mixed signals about how she should respond to the city's worsening financial crisis.

While Dixon enjoyed the support of nearly nine out of 10 voters, District residents remain sharply divided about whether the mayor-elect should initiate cuts in city services or tax increases to balance the budget, according to an analysis of citywide returns and exit polling conducted Tuesday for The Washington Post.

Nearly half of those voters questioned in exit polls said they favored increasing city taxes over service cuts if that would help erase a city government deficit that next year could approach $200 million.

However, more than a third, 37 percent, said they supported cutting services rather than raising taxes. The remainder, 16 percent, expressed no opinion.

Voter views on tax increases and service cuts broke along racial and, to a lesser extent, class lines, with blacks and less affluent District residents somewhat more likely than whites to favor tax increases over service cuts.

A majority of black voters questioned -- 53 percent -- favored tax increases, while 36 percent supported reductions in services.

According to the poll, white voters split about evenly on the issue, with 43 percent of those questioned favoring a tax increase and 45 percent supporting reductions in city services.

There were similarly modest differences when the polling results were broken down by income levels, suggesting that divisions over the best way to solve the city's current budget crisis extend across economic class lines.

According to the survey, half of those voters with household incomes of less than $15,000 favored increasing taxes to balance the budget, compared with four out of 10 residents with household incomes of $100,000 or more.

At the same time, only one-third of the Dist-rict's least affluent voters said they favored reductions in services, compared to about half of the District's wealthiest residents.

Republicans and Democrats also differed on the best approach to the budget crisis. According to the poll, Democrats favored tax increases over service reductions 51 percent to 38 percent, while 43 percent of all Republicans favored tax increases and 48 percent preferred service cuts.

Taken together, the poll results suggest that despite the enormous breadth of support for Dixon in her race against Republican Maurice T. Turner Jr., the District's next mayor may have to deal gingerly with her electoral coalition as she formulates her budget strategy.

Ronald Walters, chairman of the political science department at Howard University, said he believes Dixon can hold together her support in the months ahead.

"There is emerging a new class of young professionals who want to be involved in the political system," Walters said. "She has a potent new political force there, if she can mobilize it and put it to work."

Other observers said the magnitude of Dixon's victory -- she carried all 140 precincts against Turner, most by staggering margins -- could cushion her as she exercises her mandate to alter the size, if not the shape, of the government.

"It's an exciting moment for the District of Columbia," said Alice M. Rivlin, the chairman of a special commission that later this month will recommend deep cuts in the D.C. government payroll, among other steps, to balance the budget.

"The city has a new mayor with a very strong mandate for change," said Rivlin, a senior fellow at the Brookings Institution. "It's a chance to reexamine what the city does and how it pays for it, as well as its relations with the federal government and surrounding jurisdictions."

Others expressed some reservations this week about the strength and quality of Dixon's mandate, saying the Democrat had yet to elaborate on her reform message beyond a pledge to fire 2,000 city workers in her first year in office.

"Her first challenge is to come up with a program," said Sam Smith, a leading liberal activist and longtime commentator on District affairs.

"If you go back to the beginning of the campaign, Sharon was not indisputably the reform candidate," Smith said. "She was just another candidate running. The idea of her as a reform candidate just drifted into her as the campaign developed.

"I'm not totally convinced that she's as enthusiastic about reform as her supporters are," Smith added. "I don't see the evidence of that, aside from her promise to reduce the number of employees by 2,000. Apart from that, we haven't heard very much."

Diane Feldman, a Washington-based pollster, said yesterday that popular support for a tax increase might depend on whether it was structured as a levy on Washingtonians only or on suburbanites who work in the District as well.

"There is certainly a feeling that neither the federal government or people living outside the District are paying their fair share," said Feldman, who as Mayor Marion Barry's longtime pollster has conducted many surveys of D.C. voters.

In many ways, the flip side of the Dixon juggernaut was the overwhelming defeat for Barry in the race for one of two at-large seats on the D.C. Council, which were captured by incumbent Hilda H.M. Mason of the D.C. Statehood Party and Democrat Linda Cropp.

Barry was shut out of all but three of the District's eight wards, finishing third to Cropp and Mason in Wards 1, 2, 3, 4 and 6, which include neighborhoods with high percentages of white and affluent black residents.

Barry finished second to Cropp in Ward 5 and carried Wards 7 and 8. However, the mayor captured Ward 7 by a scant seven votes over Cropp, 9,088 to 9,081.

There were signs of Barry's political weakness in precincts across the city. For instance, while he performed best in his home precinct, 110, in Ward 7, with 1,019 votes, he failed to carry the precinct, finishing 181 votes behind Cropp and 194 votes ahead of Mason.

In Precinct 66 in Ward 5, a bellwether because of its large Democratic registration and high number of middle-class voters, Barry finished third behind Cropp and Mason.

Barry's fared worst in Precinct 12 in Ward 3, where he garnered 9 votes, in contrast to 578 for Cropp and 461 for Mason.

Mason, a three-term council member, failed to carry any of the District's 140 precincts, but finished second to Cropp in 70 precincts, a consistency that propelled her to second place in the citywide total.