FROM ALL indications, the House Select Committee on Assassinations is about to self-destruct. It was supposed to use the two-month extension granted by the House to straighten out its budget problems and organize responsible inquires into the murders of President Kennedy and Martin Luther King Jr. Instead, the situation has deteriorated into an acute embarrassment for the Whole House. Chairman Henry B. Gonzalez (D-Texas) is publicily at logger-heads with chief counsel Richard A. Sprague, whom he has tried to fire. And Gonzalez' intemperate performance has alienated the rest of the committee, which has come together in Mr. Sprague's defense.

It is hard to see how, with the current cast of characters, the panel can be held together even until the end of March. Indeed, feelings are now running so high that the whole enterprise could fly apart in a matter of days. Mr Gonzalez seems determined to force his colleagues to choose between himself and Mr. Sprague - but, if it comes to that, Mr. Sprague seems likely to have the votes. However lukewarm some committee members may have been about their counsel's agressive conduct in the past, they now seem to think that he has learned to operate more quietly and carefully, and that Mr. Gonzalez' indictment is overdrawn. Yet, even if Mr. Gonzalez should admit defeat and step aside, any prudent man who assumed the chairmanship would demand the freedom to choose a new staff in the interests of control and credibility. Thus, if the panel is to be salvaged, both Mr. Gonzalez and Mr. Sprague may have to go. If they don't recognize this, unhappy chore of bearing the message may well fall to Speaker Thomas P. O'Neill.

Is there any real reason to try to rescue the committee for itself? A serious investigation, especially of the King case, might resolve some of the questions that persist - though it would be naive to think that any amount of official investigating could satisfy all the devotees of various theories about the two murders. On the other hand, congressional committees are, at best, ungainly vehices for arriving at even partial enlightenment in such affairs. Moreover, the current inquiry has shown strong signs of political adventuism from the start, any may now have become too farcical to be perpetuated in any form. Some of the panel's more thoughtful members disagree. So do some of the less thoughtful - unfortunately, including D.C. Del. Walter Fauntroy - who persist in casually tossing around new scraps of "evidence" of this or that to stir up support of pressing on. But the House will have no justification for authorizing a longer, more extensive inquiry unless the committee can work its way out of current mess. And that will require far more common sense and restraint than anybody has shown so far.