The candidate paused in the doorway of the Sheraton Wayfarer dining room just long enough for a man paying a bill to give him the once-over.

"Say, you look familiar," the customer said to the candidate, a tall, lean, athletic senior citizen who wears his hair in a gray fringe and maintains the quiet bearing of a bank president or a professor.

"I'm Senator Hayakawa from California," the candidate responded, in jest, extending a hand. "Oh yes," the customer responded. "I'm a big fan of yours."

Sen. Alan Cranston had begun another day in his campaign for the presidency, 1984.

It is a quixotic sort of campaign, now in its embryonic stages. It is the campaign of a senator who is held in high esteem by his peers, was three times elected to the number two Senate Democratic leadership position, and is frequently in the forefront of such issues as the nuclear arms freeze and the opposition to the constitutional amendment requiring a balanced budget.

Yet it has many of Cranston's admiring fellow Democrats wondering why he is running: Is he serious? Does he really think he can win?

It is a campaign in which the candidate, for all his determination, is at times so low-key that he occasionally impresses people as lackadaisical and even indifferent, as though he is not always serious enough to make sure that everything he does, he does right.

Cranston, however, makes it quite clear that he is quite serious. Serious about running, serious about winning, serious about the issues he speaks out on as a liberal.

Yet when Cranston campaigns, his highs and lows can come back-to-back.

At a lunch with teachers Cranston was impressive, striking out at the education budget cuts and the president who proposed them and talking of his vision of what should be done instead.

But with state AFL-CIO officials at the next stop he was tentative, almost diffident. He seemed at a loss as to what to say to them; the conversation was marked by embarrassing silences that were ended only by the state federation president's effort to prompt the candidate and prod him from subject to subject.

"He has unlimited growth potential as a candidate," contends Sergio Bendixen, director of Cranston's exploratory campaign, who also conceded the unevenness of the campaign performances as well as Cranston's strengths and weaknesses.

There is the matter of image. He is 67 and in television head shots he looks every bit of it. His gauntness, plus his baldness, give him a pinched, beaked look.

He also is a world class sprinter--not a jogger--who once held the world record for men over 55 in the 100-yard dash and who still runs--not jogs--daily for the fun of it.

"People talk about age and image. That's his major handicap; there's nothing we can do about that," says Bendixen. "We can't make him younger and we can't make him prettier."

He goes on: "The other thing people say is that he can't turn on crowds. Well, that we can work on. But they don't say that he isn't substantive enough to be president. No one questions that."

Cranston likes to say that any one who has ever been elected to a city council post has had it in the back of his mind that someday he just might run for president. He says he was always awed by the presidency: it meant Washington, Jefferson, Lincoln, the Roosevelts.

But his 13 years as a senator in Washington, meeting with Richard M. Nixon, Gerald R. Ford, Jimmy Carter and President Reagan and watching them work, have taken the awe out of him.

It was in the fall of 1981 when the why-not-me? bug finally bit and he told his family and top advisers that he would take the first steps toward running for president. He says he had become increasingly upset by Reagan's policies--the domestic budget cuts and the huge defense increases, the confrontational policies with the Soviets--which started him thinking about running.

"I'd never considered it achievable before," he says. But some advisers and others whose opinion he trusts began telling him how it could be done. Now he too is a believer.

Cranston has a clear vision of how he believes he can win the presidency.

" Edward M. Kennedy is the front-runner right now," he says. " Walter Mondale is second. Then I guess you'd have to say John Glenn is third and I am fourth. Some would put Gary Hart there too . . . . I think Glenn is probably the principal alternative along with myself.

"We each start out with our home base and I think all of the candidates are in good shape in their home states. Mine is California, and that is almost 20 percent of the delegates that is needed for the nomination. So it's a good start.

"I'm further along than Jimmy Carter was at this stage before the 1976 race. And I'm told I'm further along than JFK was, too. So the early prognostications about front-runners mean very little . . . .

"It is wide open in every state in the West. I have a rolling start in the West and don't forget that California has affinities with the Sunbelt, too."

Cranston, one of the Senate's staunchest liberals, is asked if he feels his state's Sunbelt affinities will transfer to his presidential aspirations.

"You're damn right I do," he says. "I understand the economies of those states. I supported the independent oil producers, even though I didn't go along with the oil depletion allowance for the big oil companies."

Cranston has targeted seven states for special, early attention, Bendixen says. They are Iowa and New Hampshire (the first caucus and primary states), New York and Illinois (both large early states), Alabama and Washington (because he needs an early southern and western state), and Wisconsin (because he says he feels liberals tend to do well there).

Cranston plans to spend $50,000 a month for the rest of this year on the exploratory phase of his campaign. Cranston's retired Senate colleague, Harold Hughes, has agreed to be his campaign chairman in Iowa, where Hughes is still popular.

For his run in the southern and western Sunbelt states, Cranston's advisers are trying to soft-pedal his liberalism. He did vote for the B1 bomber, whose manufacturer, Rockwell, is in Los Angeles. Cranston was asked who his competition would be in those regions.

"Plainly Kennedy would not be," he says. " . . . I'd rule out Kennedy in the Sunbelt and also in the mountain West. Mondale could be competition there, but I'm not sure. Glenn would be . . . .

"People ask what the difference is between us. Well, our voting records are not greatly dissimilar. But the rhetoric of Mondale and Kennedy tends to stir passions more. I tend to be more of a reconciler."

When he catches them just right, as he did with the teachers, he scores political points. But on other occasions, he leaves them looking.

"I like him on all the major issues, but I want a leader," said one of the state's top AFL-CIO officials. "I was a trifle disappointed. He didn't come on with the fire I wanted. I wanted to hear what he is going to achieve as president . . . . I know they say he looks too old. But if he comes on with a lot of fire, it won't be a problem."

As Cranston prepared to leave his luncheon with the teachers, he got some advice. People want candidates with charisma: "They want to see someone tap-dancing across the stage," someone said.

"I don't think the American people are looking for charisma or entertainment," Cranston replied.

The questioner persisted. "Then you don't feel the need for a toupee or dark hair?"

"No," said Cranston, "then I'd start being what I am not."