EVER SINCE Walter E. Fauntroy first took the floor of the House as the District of Columbia's lone, voteless emissary to Congress, he's had this impossible dream: that someday, two-thirds of the members would vote to let the people who live here have full-fledged senators and representatives in Congress. Fat chance, said those faceless "longtime Capitol Hill observers." But yesterday, thanks to Mr. Fauntroy's faith and footwork -- and a superb campaign by the Self-Determination for D.C. national and local coalitions -- the House did say yes, with a solid 289-to-127 vote. Moreover, the members capped it with two emotional standing ovations for the teary-eyed delegate from the District. It was, as House Majority Leader Jim Wright (D-Tex.) proclaimed exuberantly, a "great day in the history of human freedom," reflecting the belief that there is "no such thing as a second-class American."

Well, you can't be sure about that -- for now it's on to the Senate, where things are a bit clubbier. Nevertheless, we like to believe that most senators today recognize that the issue is not one of political ideology, but of good democratic government, of something that is right. Certainly the vote in the House reflected that sentiment, with support coming from 228 Democrats and 61 Republicans from all points on the political spectrum.

In any event, before the Senate begins serious consideration of the measure, a brief time-out is in order, we submit, to thank those who were instrumental in building the impressive House vote. The support of President Carter, Vice President Mondale and the leadership of the House was more than lip service; the administration lobbied intelligently and diligently, as did Rep. Don Edwards (D-Calif.), chairman of the subcommittee handling the resolution, and floor manager, Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.); and, among the Republicans, John Hall Buchanan Jr. of Alabama and Robert McClory and Tom Railsback of Illinois.

With that as impetus yesterday, a cross-section of senators -- including Edward M. Kennedy (D-Mass.), Birch Bayh (D-Ind.), Charles McC. Mathias Jr. (R-Md.) and Barry M. Goldwater (R-Ariz.) -- signed a "Dear Colleague" letter urging Senate approval of the resolution. In their letter, the senators rightly emphasize that all the leading constitutional scholars who testified before the House hearings said they found no constitutional problems in letting the District have two senators.

What it boils down to, the senators' letter rightly notes, is a matter of supporting a "fundamental principle of justice for the citizens of the nation's capital." That is how so many Americans throughout the nation have reacted when apprised of the District's disenfranchisement; they recognize the wrongness of taxation without representation, and of excluding the people of the District from participation in important national decisions. The incredibly long effort for full representation -- having come this far --should not wind up crushed by an insensitive Senate. The job needs to be finished this year.