When Washington pokes fun at itself

It was the annual spring dinner of the Gridiron Club where the press, in friendly song and banter, gives both political leaders and itself a thorough ribbing.

Reporters playing the part of disgruntled Republican lawmakers, led by Robert Michel, took note of an economy that dipped deeply into a recession by singing their own version of ''We want to thank you Herbert Hoover'' from the musical ''Annie'': We'd like to thank you Ronnie Reagan For really showing us the way, We'd like to thank you dear old Gipper, You made us what we are today.

Of Anne Burford's recent treatment by the administration and to the tune of ''The Girl that I Married,'' reporters made this comment in song: While insisting - and resisting; She was left in the wind slowly twisting. If you get the headlines, it's back to the breadlines For you.

Of the much-talked-about differences among Reagan's top White House threesome , Meese, Baker, and Deaver, the Gridiron chorus sang to ''Side by Side'': Oh, they ain't just a barrel of monkeys, They're Reagan's top-ranking flunkies, With a shiv in each hand Divided they stand Side by side.

But the press didn't shy from a round of humorous self-depreciation. In the opening number - with the President and all of Washington's top brass joining with visiting publishers to watch the show - the media's singers threw some jabs at themselves to the music of ''Aida'': The Press! Keeping the columns long, Keeping the nation strong, Even when we're wrong; We know best, More or less, Hail the press.

The Democrats were in for their share of kidding, too. To the tune of ''Officer Krupke,'' the Gridiron players sang: Dear kindly Sergeant Tipper, By which we mean O'Neill, Our blarney-loving skipper, Who'd rather talk than deal.

Of John Glenn's trouble in getting started with the public as a candidate, an actor playing Glenn sang to the tune ''I Can't Get Started'': I've flown around the world out in space, I set the Senate's vote-getting pace,

The trackless void I charted, But I can't get started with you.

Of Fritz Mondale's promise to sit down with Andropov if he becomes president, the impersonator of the former vice-president sang to ''Maybe This Time'': They say Andropov, oh, he's some kind of hard case. Wait 'til Yuri meets me. I'll just tell him Stop this arms race. What a hero I'll be.

Then came Ted Kennedy's Gridiron stand-in who sang to the tune ''The Last Time I Saw Paris'': The last time you saw Teddy, My words were no, no, no. But somewhere deep inside a voice Says ''Come on kid, let's go.'' The next time you see Teddy, It may be ''oui, oui, oui.'' L'amour toujours. Toujours l'amour, I love the pres-den-cy.

There was much more: Senator Hart proclaiming that because of his ''slick campaign promoters'' and ''organizing skill,'' ''I'll run better than McGovern did.'' Senator Cranston singing of his ''youth and vigor'' and insisting, ''I'm not just another pretty face.'' And there's Claude Pepper to the tune of ''Rock of Ages,'' singing: ''Rock of aged, follow me; We will raid the Treasury.'' And, again, much more.

The Gridiron show has had a long run; nearly 100 years now. So it must be doing something right. Its success seems to lie in its ability to put Washington's so-called ''big'' people in perspective: to remind them that they are not that all-fired important. And apparently everyone comes away refreshed by this encounter with candor and geniel satire.