John B. Connally, apparently unhappy about his campaign for the Republican presidential nomination, has brought in a "pruner" to trim his staff and oversee the activities of his campaign manager.

Charles Keating, the campaign's new chief administrative officer, has fired 20 of the 160 staff members at the Connally headquarters in Arlington and more are expected.

Eddie Mahe, Connally's campaign manager, has been relieved of administrative responsibilities but will continue as the former Texas governor's chief political strategist, spokesmen said yesterday.

Although Connally has frequently complained in recent weeks that his campaign is running out of time, campaign chairman Winton (Red) Blount insisted that Keating's elevation was not a demotion for Mahe.

"Eddie is a political strategist and organizational genius," Blount told a breakfast meeting of reporters. "He will continue doing what he does best. He'll just have more time to do it."

Asked to define Keating's role, Blount said, "I'd say he's a pruner."

The staff reductions at Connally headquarters were made, Blount said, because the operation had become too fat and Connally wants to conserve campaign money for advertising.

Keating, a Phoenix businessman, until recently was Connally's fundraising chief in the southwest.

The only top-level staff member included in the first firings, which sources said may reduce the Connally headquarters staff by 40 percent, was political research director Arnold Tompkins.

The changes, press spokesman Hugh O'Neill said, represented "a belt tightening and a refocusing of the campaign."

"They looked at the whole campaign and said the primary season is upon us," he said, adding that efforts are also underway to beef up Connally field operations in Iowa, New Hampshire, South Carolina and Massachusetts.

Connally has had greater success raising campaign funds than any of his GOP competitors, having collected more than $7 million. But he has had difficulty moving his campaign from a corporate boardroom constituency into the public arena and has suffered a series of defeats in straw ballots held at party events around the country.