SENATE MAJORITY LEADER Robert C. Byrd said some encouraging words the other day about full congressional representation for the District of Columbia. When the proposed constitutional amendment comes up in the Senate, Mr. Byrd said, he will support cloture to limit debate and block attempts to amend the measure to death.

That is a key vote for cloture - and more. It sounds like a strong signal that Mr. Byrd wants the Senate to vote on the matter before adjourning on Oct. 7. Although the Senate's agenda is heavy, and long battles over energy, civil-service reform and other matters are ahead, the majority leader does not seem the least bit put off by the threat of delaying actions by a few diehard opponents of the D.C. plan. Moreover, Mr. Byrd made clear that he will have no patience with efforts to tack on unrelated amendments, such as proposed constitutional changes dealing with balanced budgets, abortion, busing and school prayer.

In short, Republican Sens. James McClure of Idaho, Orrin Hatch of Utah and Dewey F. Bartlett of Oklahoma and their allies seem to have lost the first round. They have failed to deter Sen. Byrd from bringing up the amendment this year. The question for them now is how - not whether - the D.C. representation issue should come to a vote. They can always try to stall until muzzled by cloture. Their Senate colleagues might be more appreciative, though if they would agree to some limits on debate. Then perhaps Sen. Byrd could schedule the amendment right before the tax bill. After all, taxation without representation is one central issue here.