So deep has conservatives' distrust of the Bush White House become that they greeted the extraordinary selection of William J. Bennett as Republican national chairman not as an olive branch but with suspicion of chicanery from John Sununu.

The immediate response from the right was that Sununu had tapped one of the nation's most articulate and attractive figures in order to silence him in what may be a darkening winter of Republican discontent against President Bush. Longtime friends and allies pleaded with Bennett not to take the post for that very reason.

That judgment may do a grave injustice to the White House chief of staff. But it reflects how bitterly conservatives have reacted to the rampage by Sununu, their erstwhile favorite, in the wake of Bush's budget fiasco. There will be close scrutiny whether the decision to name Bennett reflects a changed attitude by Sununu. After pondering the offer for several days and at one point turning it down, Bennett accepted the job Saturday morning.

This unexpected course of events was triggered shortly after the election by published reports that National Chairman Lee Atwater, physically disabled by an inoperable brain tumor, would seek a second two-year term. The reaction from National Committee members was that while they greatly admired Atwater's courage and would gladly give him the honorific title of "general" chairman, the party badly needs an active leader in a period of internal unrest.

There has been no lack of volunteers, including two members of the Cabinet who are among Bush's personal favorites. Commerce Secretary Robert Mosbacher would like the chairmanship, and Transportation Secretary Sam Skinner would adore it. Characteristically without checking it out, Sununu selected the just-resigned federal drug czar, Bill Bennett.

No more unlikely -- or innovative -- choice for party chairman can be found in American political annals. Bennett did not even become a Republican until May 1986, at age 42, a year after he was named the Reagan administration's secretary of education. He has never run for public office, never been involved in a campaign and probably could not pick too many members of the Republican National Committee out of a police lineup.

But Bennett became a national figure by enriching what has been the backwater education portfolio for everybody else who held it. As Bush's drug czar, he did not solve the problem in two years but surely neutralized it as a Republican problem in the 1990 election.

He has become a legitimate leader of the conservative movement, a potential presidential candidate of the future if he can ever find a way to acquire the necessary political credentials. With the party's right wing bitter at what it considers betrayals by the White House, Bennett has been mentioned as the potential challenger to a weakened Bush in the 1992 primaries.

Thus, Sununu's selection could be viewed in two ways. It could be an olive branch offerred to the right as a peace offering. Or, it could be a ploy to muzzle Bennett. Indeed, Bennett's friends see a scheme to downgrade him in a job for which he has no training and in which he can only end up as either a puppet or a renegade. At best, say these skeptics, the White House wants Bennett to bash Democrats, not preach true-believer conservatism.

The negative conclusion is caused by Sununu's wild post-election conduct, in which he has seemed intent on wreaking vengeance not on Democrats who forced the president's humiliation but on conservative Republicans who would not betray principle. The White House has oozed threats of purges against the House GOP leadership and even a primary campaign against prickly right-wing Sen. Malcolm Wallop of Wyoming. Sununu has been reported by colleagues as delighted by the defeat Nov. 6 of his blood enemy in home state New Hampshire politics, conservative Rep. Chuck Douglas.

Bennett was wary enough when asked by Sununu to inquire into his intentions. Would there be more tax increases? Would Jack Kemp stay as housing secretary? Would peace be made with Newt Gingrich and the other House conservatives? The answers were no, yes and yes.

Once ensconced at party headquarters, however, Bennett will get no parole from his two-year term no matter how Sununu's promises turn out. He also must remember his surprise two years ago when he learned, after becoming Bush's drug chief, that he would not sit with the Cabinet. But Bill Bennett has a genius in making much out of despised jobs. What's more, if George Bush hadn't put in his time as the party's national chairman, it's safe to say that he would not be president today.