As government engineers struggled today to regain control over the floundering satellite deployed by the space shuttle, representatives of the Gaithersburg partnership that operates the 5,000-pound communications satellite expressed uncertainty about potential liability if the mission fails.

An official of Space Communications Co., the satellite operator, said officials of his firm tentatively believe that the government, which deployed the satellite early today, is "ultimately responsible because they are leasing the system."

On the other hand, potential liability "hasn't been determined yet," said Laurie Tolleson, public relations coordinator for one of the partners, Continental Telecom Inc. "It depends on the cause of the problems to begin with and those haven't been established as yet." High-ranking NASA officials could not be reached for comment.

After a "perfect" launch Monday of Challenger, the nation's second space shuttle, and a similarly successful deployment of the satellite from the shuttle just before midnight, the satellite ran into problems about five and a half hours later.

A booster firing cut off early and instead of moving into a geostationary orbit about 22,300 feet over the earth, the satellite fell into an egg shaped orbit--one that would prevent the satellite from carrying out its full assignment of tasks. NASA officials worked throughout the day to activate onboard rockets to boost the satellite into its proper orbit.

Contel, the Atlanta-based telecommunications concern, Fairchild Industries Inc. and Western Union Corp. are partners in Space Communications Co., which is to operate the satellite system for the government under a 10 year, $2.5 billion lease arrangement.

Western Union, however, has agreed to sell its 50 percent stake in the venture to the two other companies as of July 1, when their stakes in Space Communications will rise to 50 percent each from their 25 percent interests.

The satellite, considered the largest privately owned telecommunications satellite ever placed into orbit, is called the Tracking and Data Relay Satellite and is leased by the National Aeronautics and Space Administration for virtually total government use. It is to be the first of two working satellites in the system, which will be supplemented by a third serving as a spare.

Both the satellite itself and its successful deployment are particularly important to the space program. The launch of the large satellite, which will spread to a span of 57 feet when its panels are fully extended, was to be a major test of the shuttle's ability to launch major private and government satellites.

And the satellite itself is designed to improve the reliability and to lower the cost of satellite communications by limiting the government's dependence on ground stations for its communications links.

Although the satellite is capable of transmitting voice, television and and analog and digital data at speeds ranging from 10,000 to 300 million bits of information per second and can handle up to 24 users at the same time, its primary function will be for the transmission of high-speed government data. A primary function of the satellite is to provide a communications link between earth and as many as 26 satellites and space vehicles, including other space shuttles.