In the West Wing of the White House and in the Carter-Mondale campaign headquarters one block away, the official attitude toward the draft-Kennedy movement is one of benign neglect.

"I'm not preoccupied with it. I don't spend a lot of time on it," Evan Dobelle, the head of the Carter reelection campaign, insists in his dimly lit office at 816 Connecticut Ave. "The people involved in it weren't with us early in 1976 and they're not with us now.

"We're not fearful of any opponent - real or imagined."

But if the president's men are not fearful of the efforts springing up around the country to draft Sen. Edward M. Kennedy (D-Mass.), they are genuinely perplexed with how to deal with them.

"Obviously, we follow what's going on. But we don't have a mandate to do guerrilla warfare from the White House," says political adviser Tim Kraft. "How would you go about organizing against a phantom candidacy anyway?"

Below the surface, there's also a thinly disguised sense of resentment about Kennedy's behavior in recent weeks - "Teddy's big tease," one adviser called it - and the amount of publicity the draft-Kennedy groups have generated.

No general strategy to combat draft-Kennedy groups, now active in at least nine states, has emerged from the White House, the Carter-Mondale campaign headquarters or the Democratic National Committee. Instead, they are being fought like brush fires. For example:

When a group of congressmen announced formation of a draft-Kennedy effort a week ago, Democratic national chairman John White, with White House encouragement, denounced the group as party wreckers. Such activities, White said, will "almost surely platter to John Connally or Ronald Reagan." Two days later, Carter told Democratic Party leaders that when he decides to run for reelection, he will contest every state and precinct - another thinly veiled warning to would-be opponents.

When it was learned that a major draft-Kennedy meeting would be held next Sunday in Minneapolis, Vice President Mondale's political backyard, Richard Moe, the vice president's top assistant, was dispatched to Minnesota to put together a Carter-Mondale reelection committee.

When reports appeared in New York newspapers that Democratic Party leaders had agreed to a 1980 primary date that would give Kennedy time to evaluate Carter's strength in the early primaries before he decided whether or not to run. Tim Smith, the reelection committee's counsel, was dispatched to Albany to met with legislative leaders.Smith insists the mission was purely a fact-finding one, but it was interpreted as a lobbying effort.

When a draft-Kennedy movement surfaced in New Hampshire, one of its leaders, Dudley Dudley, was offered a $25,000, part-time federal job. Unsure of whether she should feel flattered or insulted, Dudley, a member of the governor's executive council and a supporter of Rep. Morris Udall (D-Ariz.) in 1976, refused the offer.

Presidential adviser Kraft says the offer didn't come from the White House. But the episode proved extremely embarrasing. For about the same time as Dudley was being offered a job she didn't seek, the wife of state Sen. Robert Fennelly, one of Carter's earliest supporters in New Hampshire, didn't get a job she had vigorously sought.

Although another respected state senator, Mary Louise Hancock, was awarded the job as head of Department of Housing and Urban Development programs in the state, Fennelly was outraged. "I led the charge for Jimmy Carter in this state. We performed miracles for him. We took on the whole Democratic establishment and won," he said. "It looks to me like the Carter people can't tell their friends from their enemies. They must really want to lose."

Although a decision on whether to go ahead with a Kennedy write-in effort in New Hampshire won't be made until September, Dudley has been deluged with telephone calls from Democrats in other states.

"What we're looking at, I believe, is a genuine grass-roots draft movement," she says.

Since Iowa labor leaders gathered March 31 to launch the nation's first formal draft-Kennedy drive, similar groups have sprung up in New York, Florida, Minnesota, Ohio, Wisconsin, California, Rhode Island and Illinois as public opinion polls continue to show the Massachusetts Democrat as being more popular than the president, often a 2-to-1 favorite.

In additional, party leaders in New Jersey and other states openly talk of a growing concern about Carter's ability to win reelection.

In part, the groups are made up of liberals disenchanted with specific parts of Carter's domestic program: his urban policy, his energy policy, his anti-inflation programs and the way he has dealt with minority groups. Kennedy is their natural alternative.

But there is a far more serious porblem. Simply put, Jimmy Carter has become the Rodney Dangerfield of the Democratic Party.

"Carter seem to take the position that the problems of the country are too complex to solve," says Sergio Bendixen, a member of the Democratic National Committee from Florida. "I simply don't think that's leadership."

So far, the draft-Kennedy groups are not particularly powerful in themselves. Only five congressmen, none of them particularly influential in the House, have allied with them. And only one regular organization, the Cuyahoga (Cleveland) Democratic Party, has voted to back Kennedy.

"I don't see a tidal wave growing for Kennedy here," says Florida Democratic chairman Alfredo Duran. "Right now, the Kennedy movement is very localized and not very strong. About the only thing it has going for it is the people are very effective and hardworking political organizers.

That, and the location of the groups, haunts the Carter reelection effort. The earliest test of the 1980 campaign, for example, will come in a straw ballot at the Florida Democratic state convention in St. Petersburg Nov. 16-18. The next test comes during the January precinct caucuses in Iowa, where another draft-Kennedy group is active. The next is the primary in New Hampshire, site of other such group.

Perhaps more dangerous is the dynamics of the draft-Kennedy drive. Despite any formal of informal goahead from Kennedy, it has developed a life of its own. Almost every week a new group pops up somewhere.

Even those on Kennedy's staff are surprised at the boom for their boss. They had expected pressure for him to run, but not so early or so intense. Every day press secretary Tom Southwick gets two or three calls about some real or imagined Kennedy effort. Every day more letters come into the office.

The response is always the same. Kennedy, Southwick says, supports President Carter and expects him to reelected. A standarized letter has been written to respond to inquires. In it, Kennedy says, "Although I very much appreciate your generous support, I did want you to know that I do not intend to be a candidate for the office of president in 1980."

Some of those in the draft-Kennedy movement simply don't believe the response; others think they can force a Kennedy candidacy. Others think Kennedy in his attacks on Carter over national health insurance and oil decontrol is sending them a message.

Understandably, the Carter advisers would like a more definitive "Sherman-like" statement from Kennedy. But they don't expect one earlier than next fall.

They remain convinced, however, that he will not be a candidate, that his sense of party loyalty and timing will tell him 1980 is not the time or place for the last of the Kennedy brothers. They also believe that if Kennedy decided to run, it would so divide the party that the Democratic nomination wouldn't be worth having.

Carter's pride and stubbornness play an important part in this equation. "Kennedy is magical. His name is a legend. He is charismatic; he's handsome; he's got a tremendous style and delivery," said one Carter adviser in a revealing statment. "I think Carter admires these same things. But I think Carter believes he is all style and no substance, and he could beat him if he ever got him one on one." CAPTION: Picture, Sen. Kennedy and President Carter at a bill-signing ceremony last October. By Frank Johnston - The Washington Post