Beneath the gaze of Jimmy Carter and Miss Lillian and Woodrow Wilson and Chairman Mao and Hubert Humphrey and John Kennedy and James K. Polk and Richard Nixon and Robert Kennedy and William Jennings Bryant, Hamilton - an affectionate dog just entering puberty - bounds into the living room to nuzzle the newcomers.

His owner, a dark, intense and visibly worried young man in neat jeans and a salamander turtleneck, relaxes into a smile at the sight of the miniature collie who bears the name of his good friend and former White House boss. But the smile dies the moment Mark Siegel resumes the narrative:

"When a marriage doesn't work and you try everything, there's a way out. You don't torment yourself. Whenever you're in any kind of position in life and there are things you cannot do you don't DO them. Well, What IS the appeal of the White House?"

He looks up quizzically. "What IS the appeal of the White HOuse that makes this the ultimate intervening variable? After two weeks the glory of it is gone. It was a job. It was a hard job. If you are mesmerized by where you work, you can't function."

If you are mesmerized by where you work you can, however, stay. As the Vietman advisers stayed. As the Nixon aides stayed. As the Best and the Brightest stayed.

That is how Washington has always worked, with very few exceptions.

But Mark Siegel was, as his wife puts it, "a child of the '60s." He is 31. He saw the Vietnam war on TV. He protested that war. He worked for Bobby Kennedy. He says he believes in Kant's definition of right and wrong. "That means if everybody did it, what kind of world would it be?"

This month Mark Siegel left the White House.

People around Washington are saying ... When was the last time anyone resigned over a matter of foreign policy? It has happened before. But resignation in protest is still not a matter easily unserstood in Washington. The "Today" show, the "Tomorrow" show call Mark Siegel (in vain, so far) because Siegel is perceived in certain parts as an admirable oddity. How and why, after all, could anyone leave the White House?

He left because he was Carter's chief liaison to the American Jewish community and because he had "strong and personal reservations" about some important aspects of the administration's Middle East policy - especially the proposed arms sales to Arab countries.

He left because he claims he was provided with inaccurate information on that very subject by the National Security Council - he thinks it was deliberate.

He left because he says memos (to Hamilton Jordan) "that I had worked so hard on and in good faith" never reached Jimmy Carter. Because, in short, he realized he did not have an effective advocate's role, one that could influence policy within the White House.

But Mark Siegel looks angry only once during this interview. "Tom Barden," he says - monentarily his voice moves up and octave - "Tom Barden - he said, "This guy Siegel better decide whether he's and American or an American Jew."

Siege stops, sets his jaw. "I thought the question was repulsive. But if he wants an answer - very clearly, I'm an American Jew.

"I don't like the question, but I have no poroblem with the answer. The adjective means as much to me as the noun. And I could part with neither." A Sad Goodbye

Leaving was not initallly what he had in mind. Mark Siegel originally wanted a simple change in position. But once the press learned the news, staying at the White House, a confirmed critic of some of tis policies, no longer seemed possible.

Siegel and Jordon decided that. Then Siegel went to say goodbye to their boss.

"It was very sad," he says of his final meeting with Carter. "He was warm and generous in his comments about me ... And when the meeting was over and I'd left the office I never felt as close to Jimmy Carter as I did at that time ..."

But within the White House as well as outside, those vague, airy rumours float on by. That Mark Siegel might have been given a little push to resign. That not everyone was as sad as Siegel when he walked out the White House door. "Obviously," says Siegel, "some people are spreading stories around to discredit me."

He is worried enough about all this to take some precautions. Two tape recorders are playing in his living room - the reporter's and Siegel's.

And, in fact, these rumors have not been confirmed by anyone in a position to know for sure. Siegel denies them. And Jordon says, simply, "That's hogwash. Not true."

But the rumors do indicate: That Mark Siegel had made a few enemies along the way. That he made those enemies because of who he is, what this particular adminsitration is, and what the White House always is.

Mark Siegel doesn't know just where he's going from here. For most of his adult life he's been in Democratic politics. He says he's not going to give that up. Lately he also has been involved in Jewish concerns. He says he's not going to give that up.

"But Mark Siegel," says Mark Siegel with great earnestness, "has always been someone's right hand.

"And now Mark Siegel will be Mark Siegel." Bruiser Years at DNC

But first - a word from his wife.

"Nothing could be more antithetical in style than that 'Yes, Ma'am' southern style and Mark Siegel," says Judy Siegel in her office at the National Endowment for the Humanities. "Mark Siegel would be very good in another life huckstering on Orchard Street."

Mark Siegel's personality, some times abrasive and rough, appeared to work well enough at the Democratic National Committee, which he joined in 1972, becoming its executive director in 1974. After all, as Judy Siegel says, "The Democrats are a balky bunch. It took a lot of arm-twisting.

One does not have such a central role in the reconstruction of the Democratic Party without getting bruised and bruising . . ."

And that may have been just what Hamilton Jordan and Jimmy Carter, who got to know Siegel during those bruise years at the DNC, liked about him when they offered him a job as Jordan's deputy in the White House. The trouble was - what worked within the DNC was considered heavy-handed by many in the White House.

"Mark," says a political observer who does not love him, "Mark had very few friends at the White House. Ham Jordan definitely liked Siegel because he served as his lightning rod. But in December a group went to Ham to ask him to fire Siegel. And Jordan said, "No," because he said Siegel was smart and a good liaison to the Jews."

Jordan denies this (happened.) The Comments

And now - a word from Mark Seigel:

"I was very secure in my job qua job," he says, leaning against a leather couch, his pale eyes widening with anxiety.

But there were a few times when Siegel heard some comments in the White House.

"But I don't think most of the comments were malicious," he says. "What the motivation of the comments was, we'll never know . . . In all your work there's a time for laughter. I don't think if anyone referred to me as 'The House Jew' they meant it maliciously. Or the comments about 'My People.'

"I don't think so," he repeats, half to himself, "I hope it wasn't. . ." And Then . . . Humphrey

Mark and Judy Siegel more or less grew up together in Brooklyn. Having, by coincidence, the same last name, they were seated next to each other in Philosophy I at Brooklyn College.

At 13, he started as a volunteer for JFK. He got his doctorate in political science at Northwestern; Judy Siegel got her doctorate in English at the University of Chicago.

And then - Hubert Humphrey . In 1971, Siegel became his legislative assistant. They remained quite close, even after Siegel's departure. When Humphrey toyed with running once again in '76, he asked Siegel's advice. ("Hubert, it's like playing Russian roulette with somebody else's head," replied Siegel, who just didn't know what he should tell him).

But when Humphrey finally decided against running, Siegel went into his office, locked the door and did not come out. "I cried . . . And I don't know if I cried because I felt he'd made the wrong decision or the right decision . . ."

So his affection for Humphrey never was a secret. During the credential hearings of '72, Mark Siegel worked out of the Sheraton Park Hotel. And so did Eli Siegel, who worked for George McGovern.

And as you might expect, a little mistake was made. One day McGovern was switched through to Mark Siegel. And McGovern, according to one source, said, "Ell? Now about those six phone calls you asked me to make . . ."

And Mark Seigel responded with a series of "Uh-huh's" and "Yeahs."

"Some people," concludes a political observer with a chuckle, "some people though Mark might have been going a bit TOO far there."

And, several sources say, some people within the Carter White House resented those old Humphrey loyalties. In the Carter White House as in administrations post one loyalty is generally seen as paramount. They prefer it to have come early. Rough Times

This all has been very rough on Judy Siegel. On both Siegels, for that matter but especially on her because she is not a political animal. She wants a normal life with her husband and her two children which is why she says, "I don't like what politics has done to my life lately. I am not a glamorous person. I like not to be harrassed by phone calls."

At first there was no way the Siegel could have known that they would be inundated with phone calls. At first Siegel's main areas of concern in the White House were the DNC and the Equal Rights Amendment. Only last March did he begin to devote time to the Jewish community as the president's liaison. Then, because of circumstances, it became dominant in his work.

"I think," says Judy Siegel, "I think Mark has done a good thing for Jews. When I was in Israel this winter - I'd never been before - I was struck by how Israeli Jews were not typical of American Jews.They were stronger and tougher and leaner.

"I feel like I'm a Diaspora Jew. I feel like I'm more materialistic than I would like to be. I think it's good for Jews not to go along. To see someone who will say, "This is not right. And I will continue to participate in something that is not right."

"And it's not only good for Jews. It's good for all people." 'A Dream Made True'

Although he and his family (including a son and daughter) now attend a Conservative synagogue, Mark Siegel was brought up in an Orthodox Jewish home, the son of a seltzer man who sold soda and seltzer door-to door. He took Hebrew as a foreign language in high school.

But he, too, only went to Israel for the first time this winter. He says he was impressed by the "sincerity" of both Anwar Sadat and Menachem Begin.

A "And I was incredibly impressed by Israel," he says, leaning forward. "A dream made true . . ." The Briefing

In February Mark Siegel, among others, was briefed on the planned Mideast arms sales by Jessica Tuchman of the National Security Council.

He says he was told that the F-15's the White House wants to sell to the Saudis were "air-to-air defensive interceptors with very limited offensive capability."

He says he was told that Tabuk airfield in Saudi Arabia was exclusively civilian in function.

On Feb. 27, Siegel spoke before the Young Leadership meeting of the United Jewish Appeal, and told just that.

And the UJA audience booed Siegel. They challanged what he said.

So Siegel phoned the Defense Department that day to check all this out.

And he learned that the F-15's are "the best fighter-bombers in the world."

And that, "We are putting scores of millions of dollars into Tabuk. Hawks, Hawk Triads . . ."

Jessica Tuchman of the NSC professes herself "frankly puzzled by what happened." She says she gave out accurate information, never said the weapons were largely defensive or the airfield exclusively civilian. And she implies, therefore, that Siegel must have misunderstood.

In any case, Mark Siegel found himself increasingly disturbed by "limited areas of disagreement," like the arms sales, although he does say he agrees with "the general thrust" of Carter's Mideast policy. He worried about "the harsh rhetoric of various administration spokesmen . . ." He found, in other words - in his words - that his discontent was "a cumulative process."

On March 1 he asked for a job switch. Then he wondered about that, too. Could he, a critic, remain silent from now on? Should he critize from within? He says he found neither condition acceptable. And so he left the White House. And so the question is now: Has any part of the Jewish vote left the White House as well?

Hamilton Jordan, his old boss and friend, says "Where I failed is in not giving (Mark) enough reaction to (his memos). I felt he did have input through me. Probably more than he realized. I feel that where I might have failed is in not spending enough time giving him any reaction and the presidents." 'A Great Friend'

Judy Siegel says, "I liked having a husband in the White House. That makes me admire what Mark did even more . . ."

Hamilton Jordan says, "Mark is a great friend of mine. Nothing that happened will interfere with that." Prayers

And Mark Siegel is asked how he feels now about Jimmy Carter.

"I'm praying for him," he says, "I'm praying for him."