Word is circulating that Secretary of Education Terrel H. Bell will resign. One version says it may be even this week; another says it could be in July when he will be eligible for a federal pension.

In the last few months, he has been on a tightrope, dodging constant attacks from members of Congress, the education establishment and the New Right over the Reagan administration's attitude toward public schools.

The battering has triggered periodic rumors that Bell is about to fall, and the whispers started again 10 days ago after the White House ordered the firing of his chief deputy, William C. Clohan.

But Bell was at the Capitol Thursday defending the education cuts in the budget. And he said afterward that he has been too busy even to think about resigning. "What's that old saying about 'When the going gets tough?' " he asked with a grin.

A close associate said, "He's very happy and settled. He has no intention of resigning." But, the friend added later, "It's been a roller-coaster. One day he's ready to leave. The next, he's going to stick it out."

Thus, those close to the 60-year-old Bell acknowledge that he has considered resigning because of the recent assaults. The criticism from professional educators, they say, has been particularly tough on a man who has spent his life in public education.

After an early career as a teacher and administrator in small schools in places like Eden, Idaho, and Afton, Wyo., the native of Lava Hot Springs, Idaho, headed the public schools in Utah, and later became chief of the state college system in Utah. He served in high education posts in the Nixon and Ford administrations, when the education bureaucracy was sandwiched, and many say forgotten, in the gigantic Department of Health, Education and Welfare.

He was in Utah, heading the state college system, when Reagan tapped him for the Education Department.

Some lobbyists have scornfully referred to him as a "former public educator" because of his defense of the budget and his effort to kill off the department's Cabinet status.

Several state education chiefs criticized Bell openly at a recent meeting in Washington, and he admitted there that his philosophy of education doesn't match the administration's viewpoint.

Conservative pamphleteer Richard Viguerie called for Bell's resignation the same day Clohan was dismissed. He said Bell had failed to dismantle the department and failed "to stop the flow of federal dollars to radical groups."

While the Heritage Foundation gave the department passing marks on its one-year report card, some members of the New Right wonder about Bell's loyalty. One said the secretary seems to be "holding his nose" in defending the budget.

Friends recognize Bell's dilemma. "Ted's caught in the middle," said one. "He can't really talk about what he's done internally to fight for education or he'd appear disloyal to the president."

Department officials said Bell did battle the Office of Management and Budget to get money back for disadvantaged and handicapped children and college student aid, and to stave off some White House efforts to abolish the federal role in education.

Walter Talbot, superintendent of schools in Utah, has known Bell for nearly 40 years. He said in a telephone interview from Salt Lake City yesterday that he believes his friend "is a bit weary of the politics he has to follow."

He said, "I don't think he'd run from a fight. But he'd have to be committed personally and professionally to face all that opposition."

Onalee McGraw, education consultant to the Heritage Foundation, a conservative think-tank, said: "Secretary Bell seems to have two very conflicting fundamental loyalties. He's a member of the education community and he's a member of the Reagan team. It wouldn't be easy for most people to carry that off. He seems to have done it brilliantly and amiably because he's such an amiable person.

"But he can't have it both ways. And the problem with this deepening ambiguity is now becoming more apparent. President Reagan really does have to have somebody making his arguments who doesn't have this ambiguity."

Sniping from the right is likely to continue. Some friends of Bell believe the White House, rather than the secretary, will select Clohan's replacement.

"I'm sure it's tough on Ted," said Robert D. Benton, Iowa's chief school administrator and an old friend. "Many of the things being dismantled were put into place at his urging or when he was in authority before."

Some education lobbyists who knew Bell as an ally in his previous reincarnation as a federal school boss say they are exasperated by Bell's performance in supporting budget cuts and trying to stifle their Cabinet voice. But others say, practically, that Bell is bound to be a better advocate for education than most potential replacements.

Heritage's McGraw agrees. "In the Reagan administration did they public educators make out like bandits. They got one of their own."