While NASA's halo has crumbled away with breathtaking speed in the six weeks since the explosion of the space shuttle Challenger, and although its leadership is in transition, defenders say its backbone -- a dedicated, highly educated and stable work force -- remains unbroken.

Inside the labs, hangars and offices of the National Aeronautics and Space Administration "crescent" -- the string of 17 space centers, offices and other installations that stretches from Washington through Florida and Texas to California -- stiff-upper-lipped NASA employes insist that things look a lot worse from the outside than on the inside and that they are determined to keep the space program on track.

Scientist-astronaut Millie Hughes-Fulford, in flight training at Houston's Johnson Space Center, shrugs off questions about chaos and low morale at the space agency. "I'm busier now than I was two months ago. We've got four crews actually in training for flights and we're training like gangbusters right now."

But she estimates that her mission won't fly until "between 1988 and 1990 . . . . The trouble drums are really pounding right now." (NASA has said it will be at least a year before shuttle missions resume.)

For the first time, criticism by astronauts of the agency's safety procedures has flared into public view in recent days, with several saying they will not fly until the system is fixed.

Hughes-Fulford said, "I think change has to be done from within," and not in the open in a way that "makes things even tougher for people who are already working so hard, under such difficult conditions."

The astronaut corps and the ground flight crews at the Houston center have been put in "maintenance training," going through regular rehearsals of their duties to keep their skills honed, according to Eugene F. Kranz, director of mission operations. The center is also in the early stages of screening new astronaut candidates.

"We could certainly get into internal warfare, but our discipline as engineers is what keeps us from doing that," said Kranz.

Few institutions have fallen from such mythical heights as NASA. Many sources said they believe the fall was harder because the shuttle accident came as the agency was especially vulnerable: Its administrator was on leave because of an indictment on charges unrelated to NASA and its green acting administrator, William R. Graham, had been at the agency only two months.

NASA veteran James C. Fletcher, nominated by President Reagan last Thursday to return to the helm of the space agency, said in an interview yesterday that there are "still a lot of good people at NASA . . . . All they need is some stable leadership."

"It appears NASA is headless and rudderless," said a longtime NASA watcher for the House Science and Technology Committee. Referring to Adm. Richard H. Truly, newly appointed head of the shuttle program, he said, "Truly has got to have some breathing room . . . . Jim Fletcher will be a great stabilizing force -- once he's on board."

Recent revelations about NASA decision makers, Fletcher said, made them look "wishy-washy, and I don't think people should be wishy-washy." In the realm of public affairs, he said, "Some of the official statements make NASA look a little strange, all right." But on all such matters, he emphasized that he will reserve judgment until he has "dug a little further" into the facts.

Fletcher and sources in the Senate, which must confirm him, said they expect the process of Fletcher's FBI security clearance and confirmation hearings to take at least four or five weeks.

Many NASA supporters and employes privately attribute the agency's swift fall from grace in part to the presidential investigating commission headed by William P. Rogers. They said the panel raked NASA over the coals "prematurely" because of public pressures to show progress in investigating the Challenger disaster.

These critics contend that the panel has reversed the normal order of such an investigation: first to find the accident's cause and then to analyze the process that produced it. Although the cause is not yet officially determined, Rogers and others on the panel have pronounced NASA's decision-making process "flawed."

Fletcher, shortly before his nomination, called the commission's approach "a witchhunt." But yesterday, he backed off diplomatically. "I may have to eat those words," he said. "I'd better reserve comment" until the panel completes its report.

Fletcher, who headed NASA from 1971 to 1977, will leave a job as a consulting engineer and a post as professor of engineering and technology at the University of Pittsburgh to return to what he described as the long hours, hard work and "goldfish bowl" atmosphere of NASA.

Late last month, he remarked that he would "have to be dragged kicking and screaming" back to NASA. He took the post, he said, because "the president is a powerful persuader. He made it clear to me it was my duty."

Asked about rumors that he accepted the job only on the condition that he be allowed to replace Graham with a deputy administrator of his own choosing, Fletcher said, "No, I didn't put forth any conditions when I talked to the president. But I imagine I'll have the freedom to appoint my own people." He said he intends, however, to give Graham the "benefit of the doubt."