ROBERT POHLMAN, the city's deputy mayor for finance and a loyal member of the Barry administration, has been sounding an alarm for some time now. He has looked at the tax and spending numbers and has warned repeatedly that the District of Columbia is staring at big financial trouble. The message: Without new taxes, spending cuts or both, the city will go broke. There is every reason to believe Mr. Pohlman, and Mayor Barry has issued his own warnings about tighter times ahead. Council members, too, have been agonizing out loud about the city's bleak financial picture. But when decisions have to be made, the council takes a poke at any tax proposal and leaves for vacation. Then Mayor Barry abruptly changes his mind and cancels his own furlough proposal for government employees -- without any detailed explanation.

Mr. Pohlman could not contain his concern "about the government's credibility" as well as what he said was the failure of the city and the federal government to face reality. That reality is that the city's bond rating has been reduced, tax collections have fallen substantially behind projections, major city agencies continue to spend beyond their budgets and cash is low enough to raise the possibility of a payroll problem. But if the Barry administration and the council members all go catatonic when faced with this reality, what can residents expect of a new mayor, a new council chairman and a different council?

The candidates all talk about the issue -- and the need to monitor, trim or truly clip the size of the bureaucracy. Sharon Pratt Dixon, the only Democratic candidate for mayor who is not a public officeholder, tackled this question early on. She has called for "targeted" cuts of at least 2,000 mid- to upper-level, nontenured managers in the city government, a move she contends would generate $50 million to $100 million in savings. City agency heads are quick to dispute Mrs. Dixon's numbers, and others have suggested that maintaining certain temporary or project employees makes economic sense. David Clarke has said he opposes wholesale reductions in the size of the work force; he would make cuts in targeted departments, particularly in "front offices" of agency directors. Over time, employees in positions deemed nonessential would be trained to fill vacancies in the essential categories. Charlene Drew Jarvis has described the hiring of government workers as "out of control," but has said she sees no pressing need to order across-the-board cuts in the payroll. John Ray has said he would reduce the payroll mainly through attrition. Walter Fauntroy has said it is "not really realistic" to predict how many jobs could be trimmed, that a study is needed.

There is a fine study underway -- by an independent commission appointed by Mayor Barry and headed by Alice M. Rivlin -- and its preliminary findings are that the work force could be cut significantly: that some 6,200 positions could be eliminated over the next five years, some of them perhaps added to departments that are found to be shorthanded.

Clearly the payroll at city hall must be cut if the District is to begin to cope with its serious financial problems. The degree of commitment of each candidate to this reality should be a top concern of voters. Calls for studies and reliance on attrition aren't enough.