Although leading Senate Republicans and Reagan advisers now believe Alexander M. Haig Jr. can win confirmation as secretary of state, Senate Democratic leader Robert C. Byrd (W.Va.) said yesterday he would still seek a vigorous examination of Haig to make sure "no Cabinet appointee brings harmful baggage" that could impede his performance.

In a Senate speech, Byrd recalled the case of Bert Lance, President Carter's first budget director, who eventually had to step down because of questions about his business dealings that arose long after confirmation hearings.

Byrd said that neither President-elect Ronald Reagan nor the country can afford to have a secretary of state "crippled" by having to constantly defend himself "against evidence of wrongdoing, should such evidence be confirmed by Senate hearings."

Byrd made no allegations of wrongdoing against the former four-star general and NATO commander who also served as a top aide to former president Richard M. Nixon. But, he said, it is the Senate's duty to look thoroughly into questions such as Haig's role in the final stages of Nixon's Watergate crisis and any earlier involvement in wiretapping of government officials and reporters.

Byrd's words of caution came amid the virtual certainty, according to numerous senior Republican lawmakers and officials, that Reagan will nominate Haig next week as secretary of state.

Sen. Howard H. Baker Jr., who will be the majority leader in the new Republican-controlled Senate, has said publicly that on the basis of his own staff investigation of the various controversies surrounding Haig, the former general is "eminently qualified for the job and if nominated, would be confirmed. Haig did nothing improper. I know nothing that Al Haig did that was not honorable." Baker said he has reported his findings to Reagan's top aides.

Sen. Nancy L. Kassebaum (R-Kan.) said yesterday that Haig provided "great assistance" to the nation in keeping the government going during the final Nixon days and that Reagan, having scrutinized Haig's candidacy, should not be deterred from nominating the former general. Sen. John C. Stennis, the powerful Mississippi Democrat, also said yesterday he thought Haig would not be denided confirmation.

Nevertheless, there were private and public acknowledgments from both Democrats and Republicans that the administration was undoubtedly in for some "trying days," as one top Reagan adviser put it, when the confirmation hearings begin.

There is a possibility, sources say, that Byrd, who is not a member of the Senate Foreign Relations Committee, may try to arrange a place for himself on the panel for the confirmation. Byrd, a dogged researcher and questioner who played a key role in derailing the confirmation of L. Patrick Gray as FBI director in 1973, might pursue Haig's White House days with more tenacity than others.

On the other hand, senior Republican advisers to Reagan believe that the public may not stand for excessive Democratic hazing of Haig, who they feel brings distinguished credentials and a generally positive public image, as well as some controversy, to his post.

Sen. Charles Percy (R-Ill), the new chairman of the Foreign Relations Committee, hinted at a similar view yesterday. Emerging from a lucheon at Blair House with Reagan and incoming Republican committee chairman, Percy said that "obviously, anyone who has been in the position that Haig has been in understandably would be subject to questioning. But I don't want these hearings to become a second Watergate hearing."

Percy said Haig was respected internationally, that the eyes of the world would be on the hearing and that it would be "unbecoming" to reraise Watergate.

There were also indications yesterday that Haig would face questioning on several other matters.

Aides to Sen. Joseph R. Biden (D-Del.), a member of the Senate committee, say he is not as concerned about anything embarrassing surfacing about Watergate as he is about what kind of relationship the foreign relations panel would have with Haig.

Haig's background is in the military, when information is guarded, and Biden is concerned about how much information would be made available to the committee, how much the panel would be taken into Haig's confidence and whether Haig would seek to involve the committee in foriegn policy. Biden and Haig also have clashed in previous hearings on arms control, and the senator reportedly wonders about Haig's overall respect for both the members and the forum of the Senate panel.

Sen. Alan Cranston (D-Calif.), who is assistant Senate Democratic leader and a committee member, said he doesn't doubt that Haig will be confirmed unless some major new and damaging information is disclosed in the hearings.He said of the probable Haig nomination, however, that "this is not the best way to start a new administration" and promised "intensive delving" into Haig's past.

Aside from Watergate, Cranston said he wanted to "exhaustively" explore Haig's views on the use and limits of American military power, and the ex-general's views on human rights, arms control and nuclear arms negotiations with Moscow.

Sen. Mark Hatfield (R-Ore.), who was once on the Nixon White House's "enemy list," says he thinks Haig has been risen above the purely military view of the world and that if no bomb-shells explode at the hearings, Haig will be approved "overwhelmingly" by the Senate, perhaps by as many as 80 votes.