Rep. Marvin Leath (D-Tex.), 14th-ranking Democrat on the House Armed Services Committee, said yesterday he has launched a campaign to unseat Chairman Les Aspin (D-Wis.), "and I've got a good shot at doing it."

Leath, 55, a former University of Texas football star and a self-styled "conservative," said in an interview yesterday that he has been promised the votes of several liberals as well as several conservatives when the Democratic caucus meets next year to elect committee chairmen. Leath, a former high school coach and businessman, was elected to Congress in 1978.

"I've got a good shot at the chairmanship because Les has lost the trust of the caucus and I've got the trust of the caucus," Leath said. His candidacy is so far along that several fellow Democrats called to him as he was being interviewed in the lobby off the House floor and made such comments as, "Marv, I'm for you. Put me down."

A senior Democrat on the House Armed Services Committee, who declined to be quoted by name, said that several senior conservative Democrats have already decided to support Leath and are campaigning for liberal votes with considerable success. Rep. Charles E. Bennett (D-Fla.), third in seniority on the committee, last week announced his candidacy for the chairmanship. However, several Democrats said Leath has a much better chance at toppling Aspin.

Democrats who have criticized Aspin's leadership faulted his performance in the House-Senate conference last year on the defense authorization bill because he let more of the Senate bill be enacted into law. They have also assailed him for supporting President Reagan on the MX missile, for voting in favor of releasing funds for the contras in Nicaragua, and for hogging the spotlight through a continual stream of news releases.

Leath predicted that the Democratic Steering and Policy Committee in January will recommend that Aspin be reelected to the chairmanship for the new Congress. If Aspin is voted down by the Democratic caucus -- consisting of all the Democratic members of the House -- the policy committee is expected to recommend the next senior candidate, Bennett. If the caucus votes down Bennett, Leath will be nominated and face an up-or-down vote.

"I have no derogatory feelings about Les," Leath said. "But I just perceive Les is in trouble. There's a pretty good chance of him being unseated. And after a lot of people came to me and urged me to run, I said, 'Hey, let's go for it.' "

The Texas congressman terms himself "a conservative" who agrees with liberals in several respects, including the belief that the Pentagon must be reformed and that the Reagan rearmament program amounted to too much too soon. He said he can pull liberals and conservatives together on defense to advance the candidacy of the party's presidential nominee in 1988.