BY NOW, NEARLY everyone has heard at least some word about the financial difficulties that this and nearly any other city you can name are facing--but if there is anyone out there who still thinks Greater Washington may somehow squeak through without much pain, let Mayor Barry's latest proposed budget be entered in evidence as Exhibit A--"A" stands for Austerity. Mr. Barry's soothing words to the contrary, his financial plan for the year that will begin Oct. 1 contains harsh news; and even in this unpleasant proposal, the mayor may have glossed over some of the worst prospects on the financial horizon.

To say this is not to argue that Mr. Barry's financial management of the city has been careless or ignorant of the financial facts. On the contrary, the record up to now has been one of prudent policies aimed at stemming a national tide of municipal red ink; and there is even now a recognition in the mayor's projections of revenue that the yields from income, sales, property and corporate taxes are at low-to-no-growth levels. But if that's bad news, there is worse on the spending side: unemployment is as high as it has been in at least 35 years, and with this has come an increased dependency on the government.

So, put spending and revenues side by side-- without, Mr. Barry insists, any major tax increases or layoffs of permanent, full-time employees--and you have tighter times for all governmental services, from education to health services to housing to economic development. And still you may have red ink at fiscal year's end.

Mayor Barry's stated hope is for the city to go to a receptive bond market that will take the city's responsible management in the past as reason for a high bond rating. But will that same market take kindly to the mayor's failure to provide an appropriation in this latest budget to reduce the city's long-term debt? That debt, though not the fault of any single administration, and more of federal than local doing over long years, needs attention every year, bad or good, and the gradual retirement of it should not skip a year merely because times are bad.

As the details of this budget unfold, there likely will be less than meets the eye--and the prudent course may demand tax measures that Mayor Barry isn't talking about now. But shouldn't a just-elected mayor paint the worst case now, rather than try to apologize or re-explain new tax policies later? If things pick up, you may never find out. If that happens, of course, you may not care, either. If it doesn't, Mr. Barry may find the water hotter than ever.