The White House campaign against Education Secretary William J. Bennett can be traced to deputy chief of staff Kenneth M. Duberstein, dropping a big clue to the source of noxious internal feuding in the Reagan administration's lame-duck phase.

A renowned Washington superlobbyist, Duberstein was relied on by the political establishment to bring order to President Reagan's last days. But his own colleagues say he has carried on shrouded vendettas not only against Bennett but against Attorney General Edwin Meese III and fellow White House aides Tom Griscom and Gary Bauer. He is now even accused of undermining chief of staff Howard H. Baker Jr., who brought him back to the White House last winter. Duberstein categorically denied to us all charges.

This is no rerun of right-wing castigation of Duberstein as a liberal dating back to his first stint as the president's chief lobbyist. Current complaints against him as a stirrer of strife also come from fellow moderates, who feel the lame-duck White House is difficult enough without being made a cockpit to advance personal ambition and arouse animosity.

Duberstein's news clips dating back to 1981 contain no notes of criticism. That may reflect adroitness in wiping away fingerprints. But he unwittingly surfaced on Friday, Nov. 6, when Bennett asked Judge Douglas Ginsburg to withdraw as a Supreme Court nominee. The secretary received a call from Duberstein praising him, a conservative, for doing what the Baker moderates could not do.

Bennett's office also started receiving calls from White House reporters asking what the secretary did. Since Baker was in Tennessee for the weekend, Duberstein is suspected by Bennett of being the leaker. After Bennett's aides provided details of how Reagan told him to do what he wanted about calling Ginsburg, the secretary came under attack by White House spokesman Marlin Fitzwater for misrepresenting the president.

Tension carried into the next week, with Duberstein keeping alive a story that disconnects Bennett from his conservative base by pressing him to contact newsmen and recant his original version. One network correspondent, described by Duberstein as demanding a call from the secretary, could not understand why a Bennett aide suddenly telephoned him about an incident that by then had run its course.

Over the Ginsburg withdrawal weekend, presidential aides were stunned to read the front-page Washington Post story by its well-informed White House correspondent, Lou Cannon, quoting Baker associates that he ''became depressed'' after the Ginsburg appointment ''about his lack of effectiveness in influencing the president.''

In Cannon's and other press accounts, Duberstein emerges as strong man cleaning up Baker's mess. Unlike his chief, he is reported close to Nancy Reagan. Baker aides were furious that Cannon reported Duberstein managing the successful effort to win the president's approval of the Gramm-Rudman budget fix when in fact, they say, it was Baker.

When ex-Senate majority leader Baker gave up his million-dollar-a-year Washington law practice to steer Reagan around Iran-contra shoals, he named Duberstein as his deputy. Baker was detached from details. The 43-year-old Duberstein, who came here as an intern to New York's liberal Sen. Jacob Javits, was running the show. He even got a rare seat on the Reagan helicopter, displacing then national security adviser Frank Carlucci.

The first real trouble came when Judge Robert H. Bork was named to the Supreme Court. His own colleagues blame Duberstein for stories misrepresenting Baker as lukewarm toward Bork but bowing to Meese's wishes. He is similarly accused of incorrectly picturing Ginsburg's selection over Judge Anthony Kennedy as Meese overpowering Baker in a battle of wills, when in fact there was no confrontation. But Meese vs. Baker was accepted by the media.

Duberstein's response to our queries was unequivocal. ''Horse-bleep,'' he said, in answering whether he had telephoned Bennett to compliment him, whether he was the source of critical remarks about Baker and whether he had leaked the Meese-Baker confrontation. Was somebody out to get him, then? ''Guess so,'' he said. As for seeking to replace Baker, ''That's incorrect. Also horse-bleep.''

Duberstein is seen both at Justice and the White House as the Meese-must-go instigator. He has consciously burned bridges with Bennett in what seems clearly an effort to discredit the education chief with his basic constituency on the right, stigmatizing him as a non-loyalist who forced the nomination of a less conservative Supreme Court justice.

But what about his relationship, so cordial on the surface, with Howard Baker? ''I don't think Kenny left the big bucks to become just a deputy,'' one colleague told us. The notion Baker lacks nerve to save the president from Ed Meese's depredations is now planted in fertile Washington soil. From there it is one short step for the first lady to conclude that making her husband's last year in office bearable depends on the determined young man from Brooklyn replacing Baker.