The question is the obligatory one, not only because of a family name and connections but because of the man himself, his classic, enveloping smile, his genuinely friendly manner, his desire to be forthcoming in all things. Spend a few hours with David Eisenhower, eat a hamburger with him at the Halfway House Cafe, and you can almost hear the click of voting-booth lever. Who would not vote for this man given just the merest chance?

But David Eisenhower, seems not very likely, at this point, to give anyone that shot. "I think about politics, it's still there," he says, perhaps weary of the question and trying not to show it, "but the likelihood gets smaller every year. I found a line of work I really like, something I think I could stay with the rest of my life," that something is writing.

For the past two years Eisenhower has been working on a biography of the Supreme Allied Commander in World War II, the 34th president of the United States, Dwight David Eisenhower, the man he calls "granddad." And tonight, at the National Archives in Washington, he will be speaking on his methods and his progress (8 p.m. $3 admission, reservations suggested).

Much of the work he's done has taken place in a tiny all-white office above a drugstore in his warm sleepy town where the local newspaper prints inch-and-a-half headlines on the order of "Hot? YOU BET!" The Eisenhowers, now including 6-week-old daughter Jennie, live several miles up the coast in Capistrano Beach in a house they "blundered into" after coming out from New York in April 1977, intending to stay only a few months.

David Eisenhower is 30 now, married nearly a decade, and one gets the sense as he talks about this book that it is for him very much of watershed event. He laughs and says, "I've gone in the entirely opposite direction from my family at every turn of the road, going to college instead of West Point, the Navy instead of the Army, being the first in law school," but he also adds, more seriously, that "my life up until now has been a succession of obligatory experiences. I've never really been given a chance to prove myself. And though I'm far more interested in doing well by granddad, this is a chance to prove myself."

The book project started with informal discussions with agents David Obst. who had already signed Julie Nixon Eisenhower to a book contract. David Eisenhower had initially thought in terms of "a couple of freelance articles to finance a year off." But almost before he knew it the hyperkinetic Obst had set up a number of book presentations in New York that led to a contract with Random House.

Though defending the decision to write a book doesn't seem like the thing most authors have to do. David Eisenhower does it because for a while people picked at him about it, a situation that contributed to his leaving New York.

"People don't urge something else, like politics, on you unless they think what you're doing is not important, and that makes you question the value of what you're doing," he said, irritated. "People constantly urging you to get this aside to do something worthwhile, it became intolerable. The only person I want to listen to now is my editor."

Another contributing factor in the Eisenhowers' decision to leave the East was fallout from the Watergate affair. "After it was over, most intimates of the Nixon years were invited, actually it was almost made mandatory, to think of themselves as nicer or apart from that," he explained. "What drove us out was that we were tired of being forced, in a nice way, to be split personalities to become part of the premise that we were different or disconnected."

At this juncture Eisenhower sees Watergate as "sad, accidental and unneccesary," and feels that much of what happened is explicable "if you accept the premise that Mr. Nixon is basically a decent man who was embarrassed by the revelations of wrongdoing. What was learned wounded him, and undermined his will to continue. If he was the cynic everyone said he was, he would have persevered." And though he hasn't really broached the subject with him yet, a Nixon biography is very much in the back of Eisenhower's mind, "much more of a possibility," he says, grinning, "than politics."

It was Watergate too, in a way, that led to Eisenhower's current book project. "There was a malaise surrounding Washington," he says, "and I have the feeling that I had been acquainted first-hand with a calmer, better time and that I was in a position to write about one of its major figures."

The book which should be out within the next 12 to 18 months and may run to half a million words in rough manuscript was tentatively titled "Going Home to Glory" when Eisenhower thought of taking more of a eulogistic tone than he does now.

A confessed "microfilm addict," Eisenhower has spent months at the Eisenhower Archives in Abilene and interviewed 60 to 70 people, including his grandmother, Mamie Eisenhower. "Most of granddad's biographers saw his younger years uncritically, in the style of Huckleberry Finn," he says, "Mrs. Eisenhower has excellent recall of things that otherwise would be forever lost. She can, for instance, describe the man who taught granddad to play poker when he was 16."

Though being like's grandson has certainly helped in getting people to talk to him. Eisenhower has, for the same reason, experienced "reluctance to disclose unfavorable things. A politician in the '50s is not going to square with me in the cold light of day as he would with a journalist."

Yet Eisenhower feels he was able to attempt to deal with all aspects of his grandfather's personally, even his controversial World War II relationship with Kay Summersby. He talks with enthusiasm of the complexities of the man, of the dimensions to him that earlier biographers never fully explored, as for instance, the way "his mind was involved in a constant struggle to extend himself, get past his prejudices and be objective."

As a child, David Eisenhowever remembers his grandfather as "dynamic and forbiding, an active and intense man, judgmental and with tremendous vitality. What I'm finding out now is pretty consistent with the way I remember him. I'm not discovering a stranger."