THE SENATES 67-to-32 vote Tuesday approving full congressional representation for the District of Columbia was a tribute to the faith and persistence of all those who refused to believe that the Senate would never open its doors to two members elected from the nation's capital.

A great coalition produced this happy result. Within the Senate, the list begins with Sen. Edward M. Kennedy (D-Mass.), who sponsored the constitutional amendment with impressive fervor and skill; Majority Leader Robert C. Byrd (D-W. Va.), who steered the measure through some formidable parliamentary obstacles; long-time supporters such as Sens. Charles McC. Mathias Jr. (R-Md.), Birch Bayh (D-Ind.) and Barry Goldwater (R-Ariz.), and Minority Leader Howard Baker (R-Tenn.), who provided a vital boost in the last few days.

Among those who lobbied in the Senate corridors, special praise should go to D.C. Delegate Walter E. Fauntroy, who has made the amendment a personal cause and who campaigned as intensely in the Senate as he had in the House; to the Carter administration, especially Vice President Walter Mondale, who added strong support; and to the local and national Self-Determination for D.C. alliances and the civil-rights leaders who rallied nationwide concern with obvious effectiveness. The support of Bill Brock, the Republican national chairman, was important, too, and emphasized the extent to which the principle of elementary justice and human rights transcends the immediate calculations of partisan politics.

Another element worth noting was that many of the opponents' arguments were very weak or downright ridiculous. Sen. S. I. Hayakawa (R-Calif.), for instance, railed against the nation's capital as a "parasite" that grows rich on "tribute" exacted from "the working people" of the states. That currently fashionable view of Washington ignores the fact that working people in the District pay the same "tribute" as everyone else - but, unlike Californians, have no voice in how Congress spends their tax dollars. We might also note that the federal payroll in California is nearly twice as large as that in the District - and that much of his state's economy is sustained by federal contracts, projects and aid.

Along the same line, Virginia Republican William Scott and others complained that senators from the District would inevitably be "sympathetic to the needs and concerns of big government." Surely the interests of D.C. voters are not as predictable or single-minded as that. And surely some of Mr. Scott's own Northern Virginia constituents are just as sympathetic to federal efforts. Yet not even Mr. Scott has - to our knowledge - proposed denying them the right to vote for Congress.

Those and some even sillier objections were overwhelmed on Tuesday by the force and logic of the District's cause. The same appeal for human rights must now be made in the states - to a large extent, by many of the same advocates who triumphed on Capitol Hill. Ratification by 38 states within the seven-year limit is by no means ensured. But if the same patience and political force can be brought to bear, a long injustice can finally be ended.