The future of West Germany's generally well-liked and respected defense minister, Georg Leber, has suddenly been cast in doubt.

The reason is not so much the dramatic revelation last week of the dimensions of an espionage scandal within his Defense Ministry. Rather, it is Leber's behavior after the scandal was revealed that is the cause of concern and embarrassment within the top levels of Bonn's government.

Leber appeared to have been badly rattled by the disclosures - which first appeared in the respected Frankfurter Allgemeine newspaper last Monday. His handling of a subsequent press conference and a closed-door hearing of a parliamentary defense committee were both badly bungled.

Senior officials of Chancellor Helmut Schmidt's government have stated that Leber's resignation is not now under consideration.

Privately, however, they say that while the spy case itself does not offer grounds for his resignation he should not stay in the job unless he regains his composure.

Leber, a Social Democrat like Schmidt and a former union leader, has been defense minister for more than five years. He is popular within both the West German armed forces and the North Atlantic alliance, where he has become an important spokesman.

His uncertain future, therefore, had added significance to a rare meeting here tomorrow between Schmidt and the NATO commander, Gen. Alexander Haig.

Although Bonn officials say this meeting was arranged before the disclosure of the spy scandal, and is meant to discuss the state of the NATO alliance and prospects for the statelated East-West troop cut talks in Vienna, they acknowledge that the recent events here have provided additional reasons for the private discussions.

Haig's previous trips to Bonn have almost always been to the Defense Ministry rather than to the chancellor. Spokesmen yesterday said they thought Haig had visited Schmidt at the cnacellery before, but were not certain.

On the one hand, Haig is known to be a strong supporter of Leber within NATO. On the other hand, the espionanage carried out by the three ministry employees - who had access to more than 1,000 highly classified West German and NATO documents - is probably the worst in West Germany's spy-infested history.

In his press conference, Leber admitted that he learned of the dimensions of the scandal from the newspaper account - even though the spies had been captured 18 months ago - because he had failed to read a federal prosecutor's report that had been on his desk for more than a year. In a seemingly contradictory comment he said that he had informed NATO about the case soon after the trio was arrested.

Part of his counter-attack was to label the newspaper leak as a second "act of treason."

The following day, he spent only 40 minutes with the parliamentary committee, apparently angering a number of participants with what one newspaper described as a "silly and impertinent performance."

A few days later, Leber suffered a further rebuff when a constitutional court temporarily set aside a new law - officially supported by the Defense Ministry that allows youths to claim conscientious objector status that keeps them out of the army without challenge.

Leber's woes are not without a touch of irony, and he has pointed this out. The key figure in the spy ring - an attractive secretary - was actually hired in 1967 by the former conservative government.It was during Leber's tenure that federal security forces cracked the ring, which was viewed at the time as a major success.

He has also not been a warm supporter of the conscientious objector law, fearing it would undermine army strength. It was the left-wing of his party that supplied the main impetus for the law.