Last weekend was that annual celebration of silliness and civility here known as the Gridiron Dinner. It is an occasion when the newspaper people who comprise the membership of the club set out to mock the politicians we cover--and end up making fools of ourselves.

It occurred to me, sitting backstage between acts, dressed as a pregnant peasant woman, that there must be a Larger Meaning to this. Upon semi-sober reflection, I have discovered that there is.

It was captured in a line from a song that someone impersonating Rep. Morris K. Udall (D-Ariz.) sang: "There is no platform like a strong sense of humor." What Gridiron reminds us is that the only way to survive the pressures, strains and antagonisms of politics, and make this crazy and glorious system of ours work, is to keep it all in perspective.

The reporters' role in the Gridiron is a subsidiary one. We play hosts and put on the musical skits but, as President Reagan accurately observed, the level of our creative effort would do credit to the fifth grade of the Herndon, Va., school.

The special ambience of the event is created by throwing together politicians who are, in working hours, often at swords' points. The test is to see if they can, by their wit, strip the situation of its tension and turn the evening into one of fellowship.

There have been times when it failed, either because the tensions of the outside world were overwhelming, or because the politicians in question lacked the sense of irony to see the absurdity of their situation.

Last Saturday, it worked splendidly. In the presence of the Russian ambassador, the president of the United States sang a song mocking his own use of biblical imagery to buttress his anti-Soviet rhetoric. "I often quote the Lord," he sang, "cause how'd I scare the Commies, just quoting Jerry Ford?" Another Reagan verse suggested that when Philip Habib has brought peace to the Middle East, he might tackle a really quarrelsome area--the senior White House staff.

Sen. John Glenn of Ohio, the Democratic speaker of the evening, laughed his reputation as a tedious orator away--maybe for good--by turning the president and vice president--to say nothing of a distinguished columnist for the New York Times --into helpless straightmen for a monologue that can fairly be called a triumph.

Gridiron reminds us that, in the eyes of history, even the most inflated of personages in this city are bit players. As Sen. Bob Dole, the GOP's speaker, put it, quoting Oliver Wendell Holmes: statesmen and pundits "lead the parade in the same sense that small boys who jump in front of the circus parade lead it through town. When we turn off to head home, the parade goes on."

Personal relationships of the kind that are fostered on such light-hearted evenings really are essential to making government function. In a conversation after the dinner, I heard a story that shows how important such friendships can be in large-scale government achievements, like last week's passage of the measure to ensure the financial future of the Social Security system.

Last Christmas, the prospect of a bipartisan agreement on Social Security seemed remote. The commission that was assigned to draft such a proposal was on the verge of breaking up.

One thing that kept it going was the friendship of Dole and Sen. Daniel P. Moynihan, both commission members, and the link to the White House Moynihan enjoyed through his one-time Harvard prot,eg,e and live-in baby-sitter, David A. Stockman, the director of the OMB.

Perhaps an even more significant and less public back-channel of communication linked Richard G. Darman, a special assistant to the president, and Robert M. Ball, the former Social Security commissioner who was the key strategist for the Democrats on the commission.

Ball and Darman formed their friendship in a bizarre moment of the Nixon administration, when some overeager politicians on his White House staff tried to grab credit for a Social Security benefit increase by sending out a red-white-and-blue insert, with Nixon's picture, with every Social Security check the month the increase went into effect.

Ball threatened to resign as Social Security commissioner if they did that. Darman, then a young assistant to Health, Education and Welfare secretary Elliot Richardson, was the one who countermanded the White House order and saw to it that a less gaudy notice went out with the checks.

Through the years, though Ball became an adviser to the Democrats and Darman moved onto the Reagan White House staff, each remembered that in a crunch he could reach out to the other.

Their friendship helped rescue the Social Security system. Like the Gridiron Dinner, it demonstrates that there are occasions when politicians and reporters--even disguised as pregnant peasant women--do manage to rise above themselves.