The man qualifies as an authentic political giant-killer. In 1971 in the Senate Democratic Caucus, he won the job of party whip by defeating the incumbent, Edward Kennedy. In 1976, he had to turn back a challenge from Hubert Humphrey before Senate Democrats elected him their leader, the position he has held continuously from then until now.

But for 16 years the Washington knock on this successful underdog has been remarkable for its harsh consistency: West Virginia Sen. Robert C. Byrd, goes the capital consensus, has won favor from his Senate colleagues by doing favors for them. Without a colorful personality, he has often been written off as a master tactician lacking either a grand strategy or any articulated vision of national purpose.

That capital consensus is about to take it on the chin. This Congress will almost certainly move to end the public disgrace of legalized extortion we now employ to finance our congressional campaigns. Absent a national scandal, elected officeholders have been notoriously reluctant to monkey with a political system so divinely inspired as to have put them in office. But radical reform now appears almost inevitable. Both advocates and opponents of limited public financing of congressional elections agree that credit for this historic overhaul of campaign finance must go primarily to one man: Robert Byrd.

That task will not be an easy one. Major beneficiaries of any existing order are not customarily keen to tamper with the status quo. In area code 202, that list would include most organized interests with their own postage meter and political action committee. If not vision, what has led Byrd to this mission? The principal motivations for the majority leader's commitment to change look to be institutional and personal.

The institution about which Byrd manifestly cares a lot is the Senate. And the Senate is not working. One major reason is campaign money, its feverish pursuit and its unchecked growth. Because he is responsible for the scheduling of legislation for Senate floor action, Byrd confronts his colleagues' pervasive preoccupation with raising funds for their reelections, sometimes four years away. In an interview, the Senate leader described the daily entreaties directed at him: ''Please, no votes tonight . . . no votes on Monday . . . no votes after 4 p.m. on Thursday. . . . I've got a fund-raiser scheduled in Los Angeles. . . in New York . . . in my home state.'' Few would argue with Byrd's sad judgment that the Senate has become a place of ''part-time legislators and full-time fund-raisers.''

The personal angle pushing Byrd is just that. He asks an interviewer, ''Do you honestly think that a butcher could get elected to the Senate today? A garbage collector? A small grocery man? A welder?'' Listing his own previous occupations, Byrd emphatically makes his case why ''we cannot turn over our democracy to an aristocracy of money.'' The present system increasingly requires candidates either to have independent wealth or friends and associates with wealth. In 1982, when his Republican opponent was a Sears Roebuck heir who had the independent support of the National Conservative Political Action Committee, Byrd got firsthand exposure to what it takes to raise $2 million. Of contemporary fund-raising he says, ''We end up spending time with people only because they can give money to us.''

The existing system for congressional fund raising has no admirers and only a handful of defenders. Opponents of public funding for legislative campaigns regularly charge that such a plan would punish challengers and reward incumbents by limiting the amounts all candidates could spend. This argument is slightly disingenuous, coming as it frequently does from political action committees whose contributions now go to incumbents over challengers by a ratio of 6 to 1. Also overlooked is that two of the three executive incumbents -- Gerald Ford and Jimmy Carter -- who have run under public financing have lost.

Whether Byrd succeeds in his crusade ''to restore public faith in the system'' may depend in large part on the Republican Senate leader and presidential candidate, Bob Dole of Kansas. Dole once told The Wall Street Journal: ''When these political action committees give money, they expect something in return other than good government. . . . Poor people don't make political contributions. You might get a different result if there were a poor-PAC up here.'' Those are strong words that Dole will have a chance to back up soon when the Senate confronts Byrd's revolutionary notion that, in politics, money may be a good servant but it is a brutal master.