Defense Secretary Richard B. Cheney, citing cost overruns and major management problems, yesterday gave the Navy three weeks to show why its top-priority aircraft program, the A-12 "stealth" bomber, should not be canceled.

"The A-12 program is in serious trouble," Cheney wrote in a memorandum to Navy Secretary H. Lawrence Garrett III. "The apparent schedule slippage, cost growth and management deficiencies in this program are intolerable. If we cannot spend the taxpayers' money wisely, we will not spend it.

"I direct you to show cause by Jan. 4, 1991, why the department should not terminate the A-12 program and pursue other alternatives," Cheney continued.

The harsh letter came less than two weeks after the Navy fired two admirals and a captain for mismanaging the service's expensive new carrier-based bomber, which is behind schedule, over budget and has performance problems.

Each plane could cost $100 million, according to some estimates. Earlier this week, the Pentagon's inspector general reported the program and its contractors are the subject of a criminal investigation.

"Cheney is ordering the Navy to show him why we should keep this program, not how they can fix it," one Pentagon official said. "The Navy needs to meet with the contractor and see if it can be salvaged."

The A-12 program became a major embarrassment to Cheney earlier this year when the Navy revealed serious problems with the aircraft just days after Cheney, using Navy information, gave the program a clean bill of health before Congress in his review of new military airplanes.

The internal Navy report that led to the three dismissals criticized the weapons-buying "culture" of the Pentagon in which obtaining funds and sustaining programs become more important than identifying and correcting problems. It is a pattern that has been repeated in dozens of major weapons programs in recent years.

In addition, the Pentagon's acquisitions chief, John A. Betti, resigned this week, partly as a result of harsh criticism from the inspector general that he failed to adequately monitor and report the program's failings.

The Navy informed Cheney of none of the problems last year when he reviewed the program as a result of budget restrictions. Cheney shaved the Navy's request from 854 to 620 planes for about $52 billion, according to officials. Detailed cost estimates of the program have not been released by the Pentagon because officials have refused to relinquish its classification as a secret program.

A Navy spokesman said last night, "They have asked us to provide information on the program, and we will do that."

Cheney ordered the top Pentagon and Navy acquisition chiefs, as well as the Defense Department's senior legal counsel, to meet with the two primary contractors on the program, McDonnell Douglas and General Dynamics.

Cheney said that if he decides to cancel the program, the Navy will be forced to find an alternative aircraft.

"The A-6, our current carrier strike plane, is aging, and we must move ahead with an alternative that incorporates the technological advances necessary to maintain U.S. naval air superiority," Cheney said in the memo. "Older, slower and less maneuverable A-6 planes will be less able to penetrate enemy defenses and conduct their attacks."

Large numbers of the A-6 Intruders are now deployed on aircraft carriers in the Red Sea, North Arabian Sea and other nearby areas in support of Operation Desert Shield. The A-6, as well as the A-12, which incorporates some of the same technology used to make the Air Force's B-2 bomber less detectable to enemy radar, is designed to destroy enemy ships or ground targets.