Continued disatisfaction by many House members with critiques of Democratic-inspired programs by the Congressional Budget Office may prompt Congress to put some clamps on public appearances by the office's director.

Rep. Robert N. Giaimo (D-Conn.), chairman of the House Budget Committee, said yesterday that he and other House members, apparently including the leadership, are upset that CBO's director Alice Rivlin oversteps her mandate by making policy statements rather than confining herself to independent analysis.

Giaimo said in an interview that he is trying to construct "guidelines" to govern how the agency should release its reports to the public.

There appears to be no similar unhappiness among members of the Senate Budget Committee with the way Rivlin is handling her job, although several years ago she angered both House and Senate committee members with a speech she gave criticizing President Ford's budget practices with regard to Congress.

The latest flap was touched off three weeks ago when Rivlin held a press conference to release a CBO report on President Carter's energy program that said his plan's estimated energy savings were "overoptimistic."

She told reporters there "has been a lot of talk of 'sacrifice' or of the 'moral equivalent of war,' but one doesn't see it in this plan.

That press conference angered many House Democrats, including speaker Thomas P. O'Neill (D-Mass.). Giaimo said he was approached by many of his colleagues who said they were "distressed" that policy statements were being made by the Congressional Budget Office in press conferences.

The Congressional Budget Office was set up as part of the two-and-a-year-old congressional budget process to provide objective and independent analysis of budget and economic issues for the House and the Senate.

Rivlin, a well-known economist, has headed the office since its inception.

She said in a telephone interview yesterday that she has "no desire to do anything in my handling of the press that is not what Congress desires. I didn't think I had."

She added that "an objective, independent Congressional Budget Office is what the law intends and what Congress should want."

Giaimo contended that it is not a question of the independence of the budget office or "of freedom of speech. It is a question of who should speak for Congress."

He said he thinks it is necessary that the CBO make independent analyses that are available to the public. He said he is concerned that CBO officials release those reports to the public at press conferences.

"She (Rivlin) has to maintain a lower profile. If she doesn't, she could be threatening the budget process," Giaimo said. "Not everybody is happy with us, with the budget process or with CBO. When they get unhappy with her, they come crying to me."

Giaimo's budget committee had more trouble than usual this year getting a budget through the House. The first attempt to write a 1978 budget broke down and was returned to the committee.

While Giaimo said that it is public policy pronouncements - and not objective analysis - that upsets him and the leadership an example he cited of Rivlin upsetting the House leadership dealt mainly with CBO's estimates of the impact of a program differing from the House leadership's claims.

Giaimo noted that Majority Leader Jim Wright (D-Tex.) got angry last winter when Rivlin said her office estimated the government could not possibly spend as much on public works projects in the current fiscal year as the House leadership program estimated.

While Rivlin's relationship with the Senate Budget Committee appears to be a good one now, she has had stormy dealings with both groups in the past.