The White House, struggling with ways to head off draft-Kennedy-for-president sentiment, is trying to use haunting memories of 1968 to persuade liberal Democrats not to join a dump Jimmy Carter movement.

"A few of the people, perhaps in this room, felt Hubert Humphrey was not pure enough," Stuart Eizenstat, Carter's chief domestic adviser, told the Americans for Democratic Action. "And they fought him every step of the way. They fought him before he got the nomination. They fought him after he got the nomination. And they elected Richard Nixon."

"I belong to a race of people who never backed away from Hubert Humphrey," another Carter supporter, Paul Park, a black politician from Massachusetts, told the same group. "We're getting into the Vietnam syndrome again, and I'm scared to death."

Both remarks, designed to play on liberal guilt, came during a debate late Friday evening at the ADA's 32nd annual convention at the Mayflower Hotel. They were greeted with scattered hisses and boos.

"What Stuart Eizenstat said was very unfair and not very perceptive," commented Laon Shull, ADA's executive director. "We don't feel we beat Hubert Humphrey. The war beat Humphrey.He wasn't willing to break with Lyndon Johnson until it was too late."

The remarks, however, did hit at one of the most painful moments in the history of ADA, long the voice of the liberal Democratic establishment.

Eugene McCarthy's anti-war challenge to Lyndon Johnson rose largely out of the ranks of ADA and student groups in 1968. When McCarthy, a former Minnesota senator, finished a surprising close second in the New Hampshire primary, Johnson announced his retirement. Eventually, ADA endorsed Humphrey over Republican nominee Nixon, but liberal defections are often credited with his defeat.

The White House apparently feels that the same liberal discontent that damaged the Democratic administration in 1968 will fatally injure Jimmy Carter's reelection effort. Their answer, in speeches and hallway lobbying at the ADA convention, is to picture Carter as a well-intentioned liberal, serving in office during a time when the public's mood has turned conservative.

The president, Eizenstat said, has fended off right-wing political pressure by steering "the ship of state in a progressive direction under unbearable difficulties.... And the mood of the country would send that ship of state in the wrong direction."

His remarks came only hours after an ADA political commission recommended the organization commit itself to creating "an irresistible national mandate" to make Sen. Edward M. Kennedy (D-Mass.) a candidate for president.

Carter forces have little or no hope of getting the support of ADA in the early rounds of the 1980 campaign. The 55,000-member group has been voicing its outrage over his domestic programs each of the last three years.

"It is evident that what pretends to be a Democratic administration has deliberately and methodically chosen Republican policies," historian Arthur Schlesinger Jr., told the group in remarks prepared for delivery last night. "To find a Democratic president as ideologically conservative as Jimmy Carter, you have to go back nearly a century to Grover Cleveland."

Schlesinger, a special assistant to President Kennedy, charged that Carter has adopted the energy and inflation policies of Gerald R. Ford.

"The Democratic National chairman (John White) tells us that if we oppose Carter's renomination, we will elect a Republican president," he added. "That is no great threat. The fact is that we elected a Republican president in 1976."

The leadership and much of ADA's membership apparently shares Schlesinger's view. "We oppose an election in 1980 between two Republicans," said Joseph Rauh, a Washington attorney and longtime ADA leader. "What the situation is coming down to is an election between a Republican on the Democratic ticket in 1980 and a Republican on the Republican ticket."

Rauh and most other ADA leaders firmly support a draft Kennedy movement.; A Kennedy candidacy, Schlesinger said, would be greeted with "a national outpouring of support."

But, he added, "as a friend and associate of his brothers, I must confess deep personal apprehension about his standing for the presidency. He faces a decision of enormous human complexity and risk. We cannot lightly demand that he make this decision."

Another lingering fear was expressed repeatedly in hallway arguments among the group's practical politicians. That was if Kennedy stands by his current decision not to run, a draft Kennedy drive would fracture the Democratic Party and lead to the election of a Republican president.

"1968 is still in some of our minds," and Barney Frank, a Massachusetts state representative who was lobbying to tone down the draft-Kennedy resolution to be voted on today. "What we're trying to figure out is how we maximize the chances of replacing Carter with a liberal, but minimize the damage we do to Carter if we don't succeed."

"Carter hasn't come through with the domestic and social programs we want. But at least he is someone we can talk to," said Carl Tuvin, a Democratic Party fund-raiser from Baltimore.

ADA's political judgment has not been all that good in the past. In 1948, it backed a movement to draft then Gen. Dwight D. Eisenhower for the Democratic nomination over then President Harry S. Truman. Eisenhower later won two terms as a Republican.

In other action yesterday, the ADA called for the nationalization of the energy industry, and the immediate resignation of Energy Secretary James M. Schlesinger. CAPTION: Picture 1, ARTHUR SCHLESINGER JR.; Picture 2, STUART EIZENSTAT