Two of the most influential members of the Senate announced separately yesterday that they would vote Tuesday for the constitutional amendment giving Washington residents the right to elect their own senators and representatives.

The declarations of support by Senate Majority Leader Robert C. Byrd (D-W.Va.) and Sen. Robert Dole (R-Kan.), coupled with a similar announcement expected today from Senate Minority Leader Howard H. Baker Jr. (R-Tenn.), appear to put the momentum on the side of the bill's backers.

"The momentum is good," said Bill Brock, the Republican National Committee chairman who has labored to persuade his fellow Republicans to live up to the party's 1976 campaign platform pledge to fight for District voting rights. "The odds now favor passage."

Dole's decision was called "a significant breakthrough" by Sen. Edward M. Kennedy (D-Mass.), the leader in the Senate fight to win passage for the bill. He also praised Byrd's support.

News of the announcements left Sen. Orrin G. Hatch (R-Utah), one of the opposition leaders, subdued yesterday. "I'm disappointed," he said. "It makes it tougher (to defeat the amendment). But I think it can still be won on Tuesday."

Dole was clearly a prize that both camps had sought because of his reputation and the psychological weight his decision would carry. "We hadn't even considered Byrd," said Hatch. "But Dole . . . "

Dole said in a prepared statement that he still supported the 1976 Republican platform on which he had campaigned for vice president with President Ford. "The right to vote and the right to representation is the centerpiece of any democracy - and we can improve our democracy by passing the D.C. representation bill," he said.

"I think the time has come to let the people, through the Constitution, decide" on D.C. representation, Byrd told reporters at his weekly press briefing. He also characterized the amendment's chances in Tuesday's vote as "fairly good," but warned that "even one or two votes . . . could defeat the amendment."

Somewhere between 62 and 65 senators are now considered likely to vote for the amendment Tuesday, according to sources and a Washington Post survey. Twenty-six senators appear to be definitely opposed. Two-thirds of all senators present must vote for a constitutional amendment before it can pass, so the most the supporters must have is 67 votes out of the 100 possible in order to insure victory.

If the amendment is approved - it has already been adopted by the House - it must then win the approval of 38 state legislatures within the ensuing seven years to become law.

"I'm not going to claim victory until we have it in hand," said Rep. Walter Fauntroy, the city's nonvoting delegate in the House and currently its only congressional representative. "But I'm looking forward to a historic moment a little while after 6 p.m. on Tuesday," added Fauntroy, one of the chief architects of the campaign to win passage for the bill.

The amendment's supporters and opponents generally agree that its success in winning congressional support to date has been due largely to its being linked successfully to the volatile civil rights issue.

From the moment the bill was officially brought to the floor Wednesday, the issue of civil rights was made part and parcel of the debate. Opposition to the proposal, Kennedy said then, "has seemed to arise from . . . the fear that senators elected from the District of Columbia may be too liberal, too urban, too black, or too Democratic."

Meanwhile, thanks to intensive lobbying by civil rights leaders in the home states of many senators and representatives, black voters in many cases were coming to perceive a vote against the D.C. voting rights bill as being a vote against black voting rights because of the large black vote in the District.

Black leaders such as the Rev. Jesse Jackson, Clarence Mitchell, Maynard Jackson and Washington's Fauntroy have been among those who mobilized support in states hundreds of miles from Washington. Their efforts have been especially telling in those states where senators and key representatives are up for reelection this fall.

As a result, one source noted with amusement the ironic twist given the situation: the bill may eventually pass the Senate thanks to the votes of a handful of southern senators whose home states led the opposition to civil rights legislation during the 1950s and 1960s.

For those senators so ensnared, according to a senior aide to one such senator, the position has not been particularly comfortable.

"We were besieged by telephone calls and telegrams from key black leaders in the state," said the aide. "Conceptually, (his senator) has problems with the bill. He doesn't think you should screw around with the Constitution. But he'll probably vote for it because of the calls."

The senator really has no choice, the aide continued, because "for the people in the South, if they vote against it, no matter how honestly they oppose it, they'll be called racists. And (his senator) is really trying to get away from that.

"What it has all come down to," the aide summed up, "is a black-versus-white issue. For (his senator), and for all the others, it won't help them to vote for it. But if he votes against it . . . "

Much of the opposition to the bill has come from the West, where Republican senators with the same conservative bent as many of the Democratic senators from the South labor under different constraints, one source said.

With smaller urban concentrations, fewer black voters, and no reputation for opposing civil rights on racial grounds, senators there have been able to argue against the bill's passage without fear of a whiplash.

Those who have fought for the bill's passage see the issue on moral rather than racial grounds. "It's success so far has been due to making a civil rights issue out of it," said one source intimately connected with the bill's progress in the Senate. "We've been trying to put civil rights pressure back home on these people and it has worked."

The list of southern and border-state senators supporting the bill or leaning toward voting for it is impressive: Strom Thurmond (R.S.C.); Ernest F. Hollings (D.S.C.); Herman F. Talmadge (D-Ga.); and Baker and his fellow Tennessean, Democratic James R. Sasser.

In addition to such Republican heavyweights as Thurmond, Dole and Baker, Barry Goldwater of Arizona has said he will support the bill also.

Yesterday, as the bill's backers and strategists began sensing a possible victory to cap a century-old effort to win voter representation for the District, praise for hard workers and allies was being liberally interspersed between analysis and comment.

But some of the most telling praise came from one of the bill's opposition leaders and the man he singled out was Kennedy.

"Kennedy knew what he was doing" said the senator, who asked not to be named. "He knew it was a good issue and he has played it right. And if it doesn't win this year (in Tuesday's vote), he'll be back with it next year, and the next."

That senator and others predicted, however, that victory in the Senate is by no means a guarantee of a victory in 38 state legislatures that is needed to amend the Constitution. There, the opposition senators' concern about dilution of a state's power by the addition of two more senators and another representative will be keenly felt.

"I don't think I should vote to dilute what little effect Louisiana has up here," said Russell B. Long (D-La.) in a broadcast interview recently.

In that context, the opposition was not concerned.

"It's just a lot of presidential fever going on," one senator said in dismissing Dole's announcement and the possibility that Baker would announce his support today. "Because otherwise none of them would vote for it."