Key members of Congress angrily attacked NASA yesterday for what one called a "cult of arrogance" and "conceit" that led to the Jan. 28 shuttle accident and called for punishment of agency officials found by the presidential commission to have been responsible for the disaster.

As House and Senate committees began hearings on the Challenger explosion and the nation's crippled space program, members acknowledged that they had failed in their oversight responsibilities and pledged to place the National Aeronautics and Space Administration under tougher scrutiny as it tries to carry out the sweeping changes urged by the commission.

Members of the Senate Commerce, Science and Transportation Committee pressed commission Chairman William P. Rogers for the names of NASA officials responsible for the management and communications breakdowns highlighted in the commission report released Monday.

Representatives and senators also questioned Rogers about the prospect of criminal negligence charges against agency officials. Sen. Ernest F. Hollings (D-S.C.) alleged that one official -- Lawrence B. Mulloy, former head of the solid rocket booster program at Marshall Space Flight Center in Huntsville, Ala. -- was guilty of "willful gross negligence."

"There is this whole culture that grew up in NASA . . . this cult of arrogance, of hubris, of conceit -- that they knew it all," said Rep. James H. Scheuer (D-N.Y.), during a House Science and Technology Committee meeting. "How do you change this?"

"I think we need something a little stronger in terms of assurances that these individuals will not be allowed to participate in any material way in NASA decisions in the future," said Sen. Donald W. Riegle Jr. (D-Mich.).

Rogers, former secretary of state and attorney general and once a prosecutor in New York, said the failure was in the system. "I'm not sure picking out any scapegoat and prosecuting would serve the national interest," he said.

Rogers agreed that individuals at fault in the Challenger accident should be held to account, but said the matter should be left to the NASA administrator.

"I don't believe there was any venality here and I really don't believe there was any gross negligence," Rogers said. "It's not beyond the realm of possibility that some ambitious prosecutor might try to do that [bring criminal charges]. But I don't believe it would be successful and I don't think it would be in the national interest."

Mulloy, who was singled out in the report for misleading the commission, disputed those charges in brief comments yesterday to the Associated Press in Huntsville. "I can assure you I told the truth when I testified, without knowing what the exact testimony was," he said.

As for further comment, he said: "I'll decide later when there's something to talk about."

At another point yesterday, Hollings angered Rogers with repeated questions about a persistent rumor that the White House had pressured NASA to launch in time for President Reagan to mention the mission in his State of the Union address, which was scheduled for the evening of Jan. 28.

Rogers first responded that in hundreds of interviews under oath, "the answers without exception were 'nothing like that happened.' "

When Hollings pressed the matter, Rogers, his voice rising, challenged Hollings to produce evidence or stop repeating the rumor. "There isn't one scintilla of evidence . . . . If you can prove it, I'll come back here and apologize."

The harsh criticism of NASA, coming from two committees that have been among the agency's biggest boosters, marked what some called the beginning of a more distant relationship between the space agency and Congress. Some members noted that launch schedule pressure, cited by the commission as a major contributing cause of the accident, had been accepted and in some cases encouraged by Congress as part of an effort to make the shuttle self-supporting.

"There was a fairly significant failure by the people who were providing policy direction to NASA," said Rep. Robert S. Walker (R-Pa.).

While most members praised the Rogers commission for pinpointing causes of the Challenger accident, there was concern expressed that some of its recommendations -- such as vertical test firings of a new solid rocket booster and an emergency escape system in the orbiter crew cabin -- could crimp the agency's plans to resume shuttle flights in July 1987.

Vertical test firings, for example, would cost $15 million to $20 million and take more than 15 months, one knowledgeable congressional staffer said. This would require a mammoth new 200-foot test stand to support an elevated upside-down booster rocket that weighs 1.3 million pounds and generates 2.5 million pounds of thrust.

"Vertical test firing is going to be a lot of trouble and be very expensive," said the staffer, who asked not to be identified. "There's no existing test stand that you could do this at."

Rep. Bill Nelson (D-Fla.), chairman of the House space subcommittee, said yesterday that the vertical tests alone could take "upwards of two years" and pressed commission Vice Chairman Neil A. Armstrong about whether the panel thought they were feasible.

"I am prepared to do what is reasonable to ensure the safety of the shuttle," Nelson, who flew on the shuttle last January, said in an interview yesterday. "But if making it safe means you never fly again . . . then what you need to do is balance the need to get back in space . . . .

"Will NASA be nitpicked to death and never fly again?" he added. "We ought to be raising that question.