CAN IT REALLY be that Greater Washington -- so long a blissful pocket of resistance to the most serious ravages of inflation and unemployment -- is going broke? It could happen right here, in short order. That was the warning yesterday from some highly regarded specialists who looked into the financial future of the region's governments and didn't like what they saw. And even as this special task force was sounding the alarm, Mayor Barry was staring at immediate trouble in the city. Unless checked by dramatic moves by his administration downtown and all the other governments in the region, the story in Greater Washington could be the same heard in so many other urban areas around the country: spending up, revenues down -- and nothing in between.

Though the dollar amounts tossed around by budgeteers may not mean much to the average taxpayer, we are not talking peanuts here. Right now, Mayor Barry is operating with a budget that, if current conditions hold, is $110 million short. That, as it happens, is almost exactly what the task force, established by the Greater Washington Research Center and headed by Robert S. McNamara, had projected for the city. Add four years to this, and the task force projection shows a staggering gap of $257 million.

For the region in that fiscal year, the projection is that spending could outstrip revenues by $605 million. Put another way, that amount represents 9 percent of all projected spending -- a large tub of red ink. 2 But as the McNamara task force, the Barry administration and all the other governments in the region know full well, this figure has got to go -- by law -- one way or another; budgets have to be balanced. The question is, how do you want to pay -- in taxes or in sacrificesof services? There is no federal or state rainbow anywhere on the horizon, or even enough money to keep pace with inflation.

At least Mr. Barry has been alerted to the process in time to take a cue from other mayors and to start taking the dilemma to every group in the city that has a stake in the financial health of the District: business, labor, civic organizations, public school groups and others with interests in special municipal services.

But Mr. Barry, who has done a good job of coping with financial management up to now, is kidding himself if he thinks smooth talk and a few artful quick- fixes will do it anymore. He says he intends to "continue my limited tax policy and pursue a spending thrust that has a built-in 'people-to-people' policy and a no-reduction-in-force policy." Optimism is one thing, but the price of silver linings isn't what it used to be.

This is why the McNamara task force, with its reports of more projections and alternatives to come over the next few weeks, is performing an important function. It is issuing politically unvarnished findings that any polished politician would be reckless to ignore.