The House Assassinations Committee yesterday won a turnaround promise of "wholehearted support" from House Speaker Thomas P. (Tip) O'Neill Jr.

After a closed-door meeting with the committee's three senior members, O'Neill also told reporters, with apparent approval, that the panel will ask the House for $2.5 million to carry it through the rest of this year.

The committee has already spent $250,00 since Jan. 1.As a result, the new budget proposal would presumably mean a two-year inquiry costing some $5.5 million - compared with the initial projection of $13 million that caused so much controversy within the House last winter.

O'Neill's endorsement greatly enhances the committee's chances for survival, but the Speaker acknowledged that it still faces considerable opposition.

"They have my whole hearted support," the Speaker said after conferring with Assasinations Committee Chairman Loius Stokes (D-Ohio), Rep. Richardson Preyer (D-N-C.) and Del. Walter Fauntroy (D-D.C.). "But there is a lot of work to be done (getting votes) on the floor."

The Speaker's conversion apparently came after a private briefing for him on the information compiled thus far in investigating the murders of President Kennedy and Martin Luther King Jr. "They convinced him," an O'Neill aide said tersely.

Members of the House Rules Committee got their own backgrounding in a closed meeting with Assassinations Committee members shortly after noon.

The Assassinations Committee will expire March 31 unless it can win House approval of a new resolution keeping the investigations alive. But, before it gets to the House floor, the resolution must first be cleared by the Rules Committee.

Even Rep. Trent Loff (R-Miss.), who has been critical of the inquiry from the start, was hesitant after yesterday's briefing to say he still felt it ought to be squelched. But he made plain that he is still skeptical about the information that was laid out for him and other Rules Committee members yesterday at what amounted to "an informal, clandestine meeting."

He said such an approach had never, to his knowledge, been used with the Rules Committee before, not even during the impeachment proceedings against President Nixon.

"I presume the committee has collected some leads, some information which they're going to use to justify continuing the investigations," Lott said last evening. "Some of them are very far-fetched, very remote, in my opinion, but I am re evaluating my position."

The Assassinations Committee, Lott pointed out, has at least started to buckle down to work after being bogged down for months in disputes over its budget, its investigating techniques, and finally the unsuccessful effort of erstwhile chairman Henry B. Gonzalez (D-Tex.) to fire chief committee counsel Richard A. Sprague.