Unless the beleaguered members of the House Assassinations Committee produce some striking evidence soon, said one leading House Democrat, "they can start singing 'nearer My God to Thee."

Some congressmen would prefer to start the music right now. Stunned by internal bickering and questionable spending practices that have yet to be cleard up, the 12-member committee will die March 31 unless it can win a new vote of confidence on the House floor.

So far it has shown nothing to be confident about. It has incurred bills, paid and unpaid, of more than $300,000 since September in rushing together a bigger staff than it could afford. It has yet to hold a single public hearing in the murderers of President Kennedy the Rev. and Martin Luther King Jr. It has even insisted on secrecy for the hundreds of unanswered questions it has compiled, perhaps for fear that too many of the answers might be readily available. Instead of the public record, it showed a preference for seeking clues with polygraphs, psychological stress evaluators and other questionable gadgets.

Despite all that, the House voted Feb. 2 to give the committee roughtly two more months - until March 31 - to settle down, draft a reasonable and prudent budget and come back for a charter that would last through the 95th Congress.

The inquiry turned to opera bouffe. Appointed chairman by Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) for the probationary period, Rep. Henry B. Gonzalez (D-Tex.), who felt he should have been named chairman last year, took the assignment as a mandate to put the committee's over-extended finances in order.

Richard A. Sprague, a former Philadelphia prosecutor who had been promised complete autority over hiring and firing by Gonzalez' predeecessor, resisted, allegedly to the point of deriding Gonzalez at private staff meetings and warning staff members that they would be fired for carrying gossip back to members of Congress. One staffer, Edythe H. Baish, who had worked for Gonzalez for 4 1/2 years, brought the word back to him. He ordered Sprague dismissed Feb. 10, only to be countermanded by all 11 other committee members.

Finally, after waiting nearly two weeks in vain for the House leadership to back him up, Gonzalez submitted his resignation Wednesday in the wake of a series of bitter blasts.

Incredibly, the committee's 11 other members, or majority of them, apparently plan to address themselves to the dispute by ignoring it. They say they hope to meet today to recommend a full year's budget, adopt rules of procedure and pretend that Sprague and the rest of the staff are securely aboard the payroll.

All this ignores one of the basic questions raised by Ganzalez' attempts to fire Sprague. The committee majoriry said the chairman had no such power. The resolution that reestablished the inquiry this year explicitly stated that the authority to "employ and fix the compensation" of staffers rested with the full committee and not, as is customary, with the chairman.

But as one of Gonzalez' aides, Kelsey Meek, observed, if Gonzalez had no right to fire Sprague, then Sprague may not have been properly hired either. Only Gonzalez had certified his employment or that of the rest of the staff, for the 95th Congress.

"That's the next logical question," said Meek. "Did anybody ever have a legal job in the first place?"

The chairman of the House Administration Committee, Rep. Frank Thompson Jr. (D-N.J.), wasn't sure of the answer but said the question is far from frivolous.

"It is a legitimate argument," he said. "I may, in fact, have made a legal mistake in signing the January payroll [for the Assassinations Committee staff] . . . It's our opinion that the committee was not properly organized.

Several committee members indicated they will do their best to gloss over that at today's meeting and legitimize the staff as it stands. They are staffers and even some committee afraid that if Sprague should be forced out now, enough top-ranking members would quit with him, making it impossible to stage an evidentiary hearing and justify the committee's continuation past March 31.

For his part, Gonzales seems to have no intention of walking in and causing a stir. Althought House leaders say he is still the chairman until the House acts on his tendered resignation, he insisted in a letter to Rep. Richardson Preyer (D-N.C.) Friday that he was "no longer chairman" and thus not impowered to call a meeting of the committee "or perform any other function as a member of it."

Speaker O'Neill has said he would not send Gonzalez' resignation to the floor until he had a chance to talk with him - something the flu-stricken Gonzalez' letter to Preyer, the second-ranking Democrat on the committee, suggested that Gonzalez has no intention of changing his mind.

Submission of his resignation to the House ,could in turn, touch off fireworks, especially since Sprague is still chief counsel and staff director despite Gonzalez' attempts to fire him and the attempts of House Majority Leader Jim Wright (D-Tex.) to get him to share power with a chief administrator. Not a few House members are incensed at the thought that a chairman, one of their own, is being sacrificed for a "clerk."

"There are just two kinds of people who work here," said Rep. Charles B. Rangel (D-N.Y.), "members of Congress and clerks. Some are secretaries.Some are chief counsel of committees. But they're all clerks."

Sprague, in short, may not last much longer. But if he is to be dumped, the committee may have to be reconstituted, perhaps even under another name. There have been whispers about making it a House Judicial subcommittee, although Chairman Peter W. Rodino Jr. (D-N.J.) is said to have expressed disfavor. There also is rising sentiment for wiping out the entire investigation."We've fooled around with it so much it's just a mess," said House Rules Committee Chairman James J. Delaney (D-N.Y.), whose committee has jurisdiction over continuation of the inquiry. He expressed frustration that, after more than five months of sporadic investigating by the committee, he has no idea whether it has come up with anything substantial.

"I'd like to know if they have anything or if this is just a plain witchhunt" Delaney said. "I don't know if it's a witchhunt or not."

House leaders and committee members seem resigned to abandoning the investigation of President Kennedy's 1963 murder or at least assigning it "a very, very minor role." Evidently not enough promising information has been developed. They are working to salvage the King inquiry and are hoping to stage a hearing on it, before tackling the Sprague problem. But all that is still highy tentative.

O'Neill has said he thinks the committee will have to produce "something of sensational nature" to survive , but committee members are talking more modestly in terms of making public "what we believe are significant leads." A staffer close to the investigation said members believe they can demonstrate "the weakness of the Justice Department's (just issued) task force report in the King assassination regarding the (police) surveillance" of King before he was killed in 1968.

Exclaims author-investigator Harold Weisberg: "What's that got to do with who killed King? This gets zanier by the minute."

At this point, however, no evidentiary hearing has been scheduled. Says Rules Committee Chairman Delaney, for one, "My feeling is it [the committee] would not be continued."

Some blame former Speaker Carl Albert (D-Okla.) for appointing then Rep. Thomas N. Downing (D-Va.) as chairman last year. About to retire, Downing promised Sprague complete authority while Gonzalez stood waiting for the chairmanship . By custom, the Texan, as the original sponsor of the assisanation inquiry, should have been chairman from the outset.

Others blame O'Neill, whom they suspect of malign neglect.

Defenders of Sprague say he fought Gonzalez' attempts last month to cut the staff because it would be "immoral" to fire people already working at voluntarily reduced pay. Sprague, however, has yet to acknowledge any fault in hiring too many people to begin with.

Then there is Gonzalez, who waited 16 years to become chairman of a big-time committee. One House Democratic leader faults him for behaving too much like a heavy-handed, oldtime chairman, for not realizing times have changed in the House. But that's understandable, too.

"Look at the Texans who have been committee chairmen in the House," this congressman said. "You have got people like Goerge Mahon, Jack Brooks, Bob Poage. These are guys used to brooking no opposition, used to running over anybody who got in their way. Then Henry becomes a chairman and what happens? They won't even give him a gun, or let him fire his orderly."