LEADERS OF THE New Right are calling on Rep. Robert Bauman to resign his seat in Congress and his chairmanship of the American Conservative Union after a charge that he solicited sex from a teen-age boy. Bauman is saying that he is undergoing treatment and therapy and that, between his doctors and his priest and his wife and four children and the AA, he is on the road to recovery.

From alcoholism.

Alcoholism is taking a terrible beating in Congress these days, and Bauman is merely the latest in a long line of congressmen to blame demon rum for his troubles, thereby setting the stage for a moral comeback the minute they sober up. He has confronted accusations of criminal sexual behavior -- a mortal sin in his constituency -- by confessing to the relatively minor sin of alcoholism. Now he is hunkering down at his home on the Eastern Shore, measuring the political fallout, and vowing to remain in the race for Maryland's 1st District congressional seat.

Until last Thursday, that was considered a relatively safe seat. It was so safe, in fact, that Bauman did not even need campaign funds from the GOP, which is now offering money to help him out. Bauman's plan is to throw himself on the mercy of his loyal constituents, but the trouble is, he has not had the mercy to tell his loyal constituents the truth.

Bauman was not elected by the residents of San Francisco. He was elected by the residents of the Eastern Shore of Maryland, a conservative, traditional constituency that has sent him to Congress three times. This is a constituency that knew what he stood for: antiabortion, anti-ERA, antihomosexual rights, "profamily." Bauman was aligned four-square with the forces of the Moral Majority and the New Right and all the fundamentalist religious groups that have been holding up the Bible and holding back the tide. That is not a constituency that takes homosexuality lightly. It has, in fact, in the name of family fought in forum after forum against the rights of homosexuals to teach in schools and to adopt children. This is a constituency that has made private acts public issues.

And it's a constituency that has every right to feel betrayed. Moral Majority, in an unusual display of tolerance for the "immoral minority," is saying that it is not seeking Bauman's resignation because it's how a man votes, not his private life, that matters. But others, such as Paul Weyrich of the Committee for the Survival of a Free Congress, say Bauman is no longer a credible spokesman for conservative causes.

And it is not his alcoholism that is causing his problem. Bauman has explained that his alcoholism never caused him to miss a day of work, and moreover he hasn't had a drink since last May. He has explained far more about his alcoholism than he has about the homosexual incident with which he is charged. Moreover, after his initial press statement, he has remained silent on the whole business while stories have surfaced indicating that the FBI has reports of him being involved in other encounters with teen-age boys along Washington's gay strip. Bauman would have us believe that the March incident with which he is charged was a unique act of debauchery that occured during "the period of my heaviest drinking." That is not very easy to believe. Bauman is not some 18-year-old kid whose hormones suddenly went out of control. He is a 43-year-old man, father of four, and the act he is accused of committing is the ultimate marital kick-in-the-teeth. It is hard to believe that was done once in a drunken binge and that that's all there is to it. It is hard to believe on the face of it, and it is hard to believe in face of reports that there was a pattern of Bauman cruising the gay strip, and it is hard to believe if you know anything about the plea-bargaining process.

But the plea-bargaining process is what Bauman's constituents are getting. His final words on the subject are: "I have come to terms with my personal problem, admitted my faults, and am trying to make amends," without ever specifying which of his personal problems he has come to terms with. And the public record on the matter is simply that he cruised the gay bars for months, got caught once, and the charge will be dropped if he completes a rehabilitation course for first offenders.

Serious questions have been raised in the Bauman episode, ranging from the extent of his homosexual activity, and therefore, the extent of his hypocrisy, to the allegation that he was threatened with blackmail on at least one occasion if he did not use his congressional office to help a person out. He has not denied, explained, clarified, or amplified beyond his original statement which blamed all of this on demon rum.

Bauman is asking an awful lot of his constituents by staying in office and running for reelection. But by not telling them the full story, he is really asking too much.