FIRST IT WAS Teddy Kennedy. Now it is Hubert Humphrey. Robert C. Byrd of West Virginia - dour, efficient, politically and temperamentally cautious - bids fair to win the title of liberal giant-killer of Capitol Hill. Sen. Byrd, who was chosen Democratic Majority Leader of the Senate yesterday in a contest with Sen. Humphrey, moved up from a job (that of Democratic whip) which he had already taken away from Sen. Kennedy a few years back. It is true that in each of these contests there were special circumstances that worked to the disadvantage of his opponents. But when you have said that you still have not accounted for Mr. Byrd's remarkable success in a political environment that, ideologically speaking, appeared to be much more hospitable to a Kennedy or a Humphrey than a Byrd.

So what happened - and what does it mean? We will mention briefly a few well-known elements that contributed to yesterday's outcome: Mr. Humphrey's age and illness and the disorganization of his campaign for the job; Mr. Byrd's head start in the race, his meticulousness as a campaigner and strategist and his reputation among his colleagues as a fellow who can make the trains run on time. The reason we don't mean to dwell on any of this is that we think it is important but not crucial to an understanding of what occurred yesterday. Senate Democrats of every political stripe joined together to select a leader whose style amounted to a ratification of the particular independence they have acquired over the past several years.

That independence is owing to a lot of things - the breakdown of the rigid old Senate structure, the disappearance of some of the rigid old committee chairmen and the relatively complaisant leadership style of the outgoing leader, Mike Mansfield. But whatever may have accounted for this new way of Senate life, it is plain that a majority of its majority likes it. Sen. Byrd is generally expected to continue to make the Senate a more convenient and agreeable place, and a less harried one, for his flock. It has been supposed that the will do more for - and ask less of - the Democratic members than Mr. Humphrey might have. In one sense, then, you could almost say that the Democrats in the Senate don't want a leader, at least not a leader in the policy-making, party-spokesman mold.

From Jimmy Carter's point of view, this is probably a good thing. We mean no mortal affront to Sen. Byrd, to the new Senate whip, Alan Cranston of California, or to Messrs. Thomas P. O'Neill Jr. and Jim Wright of the Democratic leadership in the House, when we say that this is hardly a congressional team known for its capacity to articulate great issues or to stir the soul of the Democrats' national constituency. Interestingly, the Senate Republicans - in one of those quiet, coup-like things for which their congressional minions are justly famous - did narrowly upset the favored candidate (Robert Griffin of Michigan) for a more personable, outgoing and politically articulate candidate for minority leader, Howard Baker of Tennessee. But our guess is that the Baker-Griffin contest had (and will continue to have) much more to do with national Republican politics and their internal maneuverings than with Senate business or with the conflict between a Democratic administration and Republicans on the Hill.

In fact, we will take our guess on dangerous step further: if there is to be struggle of a large and serious kind between Congress and the Democratic administration, we suspect it will be between Democrats and Democrats - between those majorities which have just chosen Mr. Byrd and Mr. O'Neill to be their leaders and the Carter administration. Yes . . . we know . . . everything is sweetness and light now. But the needs of the legislators as the mid-term elections come nigh and the capacity of the administration to meet those needs may be two very different things. We mention this prospect because it will be then that the all-purpose value of the Senate Democrats' choice of leaders will be put to the test. Sen. Byrd may be just the fellow for a period of harmony and peace between the Carter White House and the Democratic Congress. Forgive us our spoil-sport cynicism - the question is whether he will still be the right fellow when the honeymoon is over.