When the House Select Committee on Assassinations was handed its proposed $6.5 million budget last month, it was done with a professional flair suggesting that every penny's worth had been painstakingly studied and justified.

In fact, it hadn't even been added up until a day and a half before it was presented to committee members Dec. 9 for their ritual approval.

"Any cut, in my opinion, would make the task impossible," chief counsel Richard A. Sprague intoned at the hearing that morning when Rep. Louis Stokes (D-Ohio) pressed him for a hint of where a few dollars might be saved.

No one need coax Sprague for any more hints. His budget is going to be cut, willy-nilly, perhaps by more than 50 per cent. The more immediate question is whether the committee's ambitious inquiry into the deaths of President Kennedy and the Rev. Martin Luther King Jr. will be allowed to proceed at all.

The change in the mood of the House since it authorized the investigation last September by a vote of 280 to 65 has been remarkable.

The committee's sponsors will ask the House Rules Committee today to clear for floor action later this week a broadly worded resolution re-creating the committee. Rep. Henry B. Gonzalez (D-Tex.), the chairman-designate, said yesterday that he simply hopes to see the resolution survive without any "crippling amendments."

Some restrictions in the name of due process seem likely. There is also talk among some members of requiring the committee to examine the existing evidence first.

Its investigators have been sent to Mexico City. It has talked of leads in Portugal. But just a few blockaway, at the National Archives, there is some 40 feet of shelf space loaded down with the physical evidence of the Kennedy assassination - clothing, bullets, photographs, a rifle - still waiting to be tested and analyzed by the committee.

"We're worse off now than if no investigation had been authorized," said author Harold Weisberg, a longstanding critic of the government's investigations of both the Kennedy and King assassinations.

"This committee hasn't been conducting an investigation," Weisberg charged. "It's been engaged in promoting itself. It's been engaged in trying to justify an appropriation which is not only unjustified but, if granted, would have been counterproductive."

Sprague proposed a staff of 170 persons. Weisberg maintains that "you cannot have effective communication with a staff that large."

At this point, the committee, which built up a staff of 73 before it had to stop hiring, has no official existence. The House Rules Committee is scheduled to consider the assassination panel's re-establishment Tuesday, with floor action expected later in the week.

The prevailing wisdom, which could abruptly, seems to be that it is too late for the House to try to put the cap back on the bottle of conspiratorial rumors and theories about the two assassinations which were promised congressional scrutiny last September. To squelch the inquiry now, even for the best of motives, might seem a blatant cover-up.

"I'm sure the Hill is loaded with people who have all kinds of doubts (about the investigation)." said Rep. Don Edwards (D-Calif.), chairman of the House Subcommittee on Constitutional Rights.

Edwards, whose subcommittee took sworn testimony in 1975 on the FBI's destruction of evidence in the Kennedy case, was one of the first to express concern about the current investigation in light of Sprague's plans to buy hidden radio transmitters, polygraphs, psychological stress evaluators and other gadgets.

But despite the spreading skepticism, Edward said, "I think it'll go throughin some modified form."

The center of contention is Sprague: his methods, his judgement, his temperament. An unsetting catalogue of many of many of the problems involved can be found in a 2 1/2-year-old report to the Citizens Crime Commission of Philadelphia, where Sprague, a career prosecutor, had been first assistant district attorney for eight years.

The 60-page study, conducted for a newly elected, incoming DA by consultant Charles H. Rogovin under a Law Enforcement Assistance Administration grant, complimented Sprague for being "without doubt one of the most skilled prosecutors in the country," but was less enthusiastic about other qualities.

The report was highly critical of Sprague's "total dominance over all activities of the district attorney's office," said the administration of the office was best described as chaos," and attacked its "primitive approach to budgeting practices" and its weak financial controls.

At another point, the study said that the office's investigative work occasionally constituted "a search for targets of opportunity, rather than action undertaken pursuant to a strategic plan."

Echoes of those same complaints keep coming up on Capitol Hill where Sprague insisted upon, and was granted, "complete authority" over hiring and firing of personnel on the assasinations committee.

He quickly asserted himself in an opening blitz of public statements, television and newspaper interviews, and even policy pronouncements about what the committee would and would not do. Critics such as Rep. Robert E. Bauman (R-Md.) charged angrily that Sprague had "virtually assumed the role of chairman of the committee."

Meanwhile, the committee, with Sprague doubling as chief counsel and staff director, spent itself into trouble. It got $150,000 - for a projected staff of 28 persons - shortly after it was created in September. But it wound up the year with a staff of 73.

None is being paid at present. Nor is any of the committee's creditors. The committee must be re-established first. But even then, under the rules of the House, it will be limited, until it gets a new budget, to spending no more than it spent in December.

Committee officials say that amounts to $84,000. According to a compilation Jan. 10 by the clerk of the House, the total is really only $67.797. Neither amount is enough to meet the committee's full-month payroll of $115,000, let alone any others bills. Committee staffers are planning to take a voluntary pay cut until the crisis is resolved.

The proposed $6.5 million, budget, which is certain to be slashed, poses other questions.

Described by Sprague as an exercise in sheer frugality a "bare-bones . . . bare-bottom . . . minimal" figure it calls, among other things, for $1,248,000 in domestic travels by its attorneys and investigators alone and $12,900 for bringing witnesses to Washington.

Put another way, that suggests a total of 24 trips to outlying precincts by House sleuths for every witness brought back to the nation's capital to enlighten the electorate at public hearings.

The budget also includes $180,000 for overseas travel, but before traveling abroad. Weisberg and others (such as former Warren Commissioner lawyer David Belin) contend. "You've got to establish the basic facts of each homicide first. They haven't done it yet. They don't know what they're investigating yet."

Chairman-designate Gonzalez professes now to be fully aware that the budget he and the rest of its members endorsed just last month is unrealistic. He says he is fully prepared , once the committee is re-established to cut the spending proposal back to the "irreductible minimum."

Adaptable to the changing mood. Gonzalez even scoffs at the $1.8 million in proposed overall travel expenses.

"It's inconceivable to me that I would go to anybody and say I need $1.8 million for future travel without saying where I'm going," Gonzalez says now.

But the real question, he maintains is the basic re-establishment of the committee, the issue expected to come before the House this week.On that score, there is suddenly a widespread ambivalence.

Rep. Richard Bollin (D-Mo.) reflects the uncertainty as well as anyone. A key member of the House Rules Committee. Bolling was responsible for aquelching the inquiry when it first came up for a hearing last spring. He opposed it in the name of the Kennedy family.

But then, he was "converted" last summer on the basis of information about the King assassination presented to him by Del. Walter E. Fauntroy (D-D.C.) and the Congressional Black Caucus.

Now, Bolling says candidly, he doesn't know what to think.

At this point, he said late last week. "I don't know what's going to happen in the Rules Committee Tuesday and I don't know what I'm going to do. I haven't had a chance to read enough to be sure of some things that may seem obvious to others."