President Reagan's nomination of Ernest W. Lefever as chief of human rights for the State Department ran into one more patch of trouble yesterday as Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) warned it could sink in a parliamentary quagmire.

"We have a fair chance to confirm him in a full Senate," Baker told reporters. "The problem is getting him up in the full Senate.

The Senate Foreign Relations Committee, which is handling the nomination, has basically two options if, as some members expect, it decides to oppose Lefever's confirmation as an assistant secretary of state.It could send the nomination to the floor with a recommendation against confirmation, or it could refuse to act. If the latter occurred, the Senate Republican leadership could only get the nomination to the floor through a motion discharging the committee from further consideration of Lefever.

At least until now, Lefever's opponents have been leaning toward letting his nomination go to the floor with an unfavorable recommendation. But the administration opposes such as strategy, according to Senate Republican sources.

This leaves the option of a discharge motion. Although possible, such a course would be "very difficult," Baker said yesterday, asserting that it has been used successfully only 15 times.

Among the procedural hurdles is the opportunity for a filibuster, and a filibuster in this case would be "almost certain," Baker added.

In his session with reporters, Baker refused to speculate on what course the committee might take. But he later told a reporter he figures there is probably now a "50-50 chance" that the committee will bottle up the nomination, leaving a discharge motion as the only alternative if the administration intends to pursue Lefever's confirmation.

Emphasizing that he supports Lefever, Baker said he will do whatever the administration wants. "If the president wants to push it, I'll do it," he said.

Lefever has sharply criticized the human rights policy of the Carter administration and has come under fire because of contributions to a research center that he headed from the Nestle Corp., a producer of infant formula that is used in Third World countries. The United States recently cast the only dissenting vote against a World Health Organization code restricting advertisement and promotion of such formulas.

Lefever has been recalled by the Foreign Relations Committee for a closed session later this week to answer additional questions about the conection between Nestle and his research group, the Ethics and Public Policy Center.

On Sunday, Sen. Paul E. Tsongas (D-Mass.), a member of the committee, said on a television program that 11 of the 17 members of the panel oppose Lefever's nomination, although he predicted that a vote on the Senate floor could be "very close."

Baker said he believes the nomination "is in trouble obviously" but added: "I think it is salvageable." He said he has told Reagan that there is still a "pretty fair chance" of confirmation.

In another development, the Union of Councils for Soviet Jews announced its opposition to Lefever despite his strong criticism of Soviet restrictions against Jewish emigration.

At a news conference, Robert Gordon, the council's president, accused Lefever of using the Soviet Jews issue as "a propagandistic tool" and said that impairs his credibility and effectiveness.

"It is not something which can be employed solely as a stick for attacking the Soviet government without a corresponding effort to promote a dialogue which can lead to the improvement of conditions in the Soviet bloc," the union said in a statement.