A majority of the delegates to the Democratic National Convention oppose the effort in behalf of an "open" convention rule and intend to nominate Jimmy Carter for president, a Washington Post poll shows.

The Post's random sampling of 591 delegates found that 54 percent oppose changing the rules to permit delegates to vote for a candidate other than the one they have pledged to support. Such a change is supported by 41 percent, and 5 percent are undecided.

The survey, begun July 22 and finished two days ago, also indicates that the delegates' view has not changed during the last week when the Billy Carter situation and the "dump Carter" movement became major news items.

The Post survey also suggests that virtually all delegates today still favor the presidential condidate they were pledged to support when they became delegates. of those surveyed, 59 percent said they were for Carter when they were chosen as delegates; today, 58 percent say they favor Carter and one percent answers "leaning to Carter." The survey found that 35 percent said they were for Sen. Edward M. Kennedy when they were chosen, and 35 percent say so today.

This result tracks closely with the actual breakdown of candidate pledges among all 3,331 delegates. Sixty percent are pledged to support Carter, 37 percent are Kennedy backers.

If there are no major changes in the 10 days remaining before the convention, the Post poll suggests that the Carter camp will be successful in defeating efforts to establish a rule that would let delegates disregard their pledges in order to nominate Kennedy or open the convention to other choices.

But while the delegates across the country still seem to be firmly behind Carter, the political community in Washington continues to see the with rumors and meetings and press conferences relating to various Democrats' efforts to "dump" Carter and find a nominee who has higher standing than the president in voter surveys.

Senate Majority Leader Robert Byrd (W.Va.) has been consulting with other Democratic senators about the presidential situation, but those who have attended meetings with Byrd say there has been no indication of any concerted action by Senate Democrats to look for an alternative to Kennedy or Carter.

But when the Byrd consultations became public, rumors flew so fast that two Carter backers, Sens. Joseph Biden (Del.) and Walter Huddleston (Ky.) felt obliged to call a press conference yesterday and declare that Senate Democrats still generally back the president.

They said they had polled about two dozen of the Senate's 58 Democrats and found all were for Carter and opposed any efford to "open" the convention. The two senators released a list of a dozen colleages, ranging from Abraham Ribicoff of Connecticut on the left to Ernest F. Hollings of South Carolina on the right, who are still backing Carter.

Sen. Paul Tsongas, a strong supporter of Kennedy, his Massachusetts colleague, said Carter's current problems have provoked a great deal of talk, but no clear consensus. Many Democrats, Tsongas said, are uneasy about challenging their own party's incumbent president and are quoting the axiom, "If you strike at the king, you must kill him."

Tsongas also noted that Democratic senators are all aware that they are prime subjects for interviews on the situation -- or for consideration as nominees. "Everybody's dressing better," Tsongas said.

On the other side of Capitol Hill, however, the maverick Democratic House members who have formed a committee -- with a $200,000 treasury -- to lobby for opening the convention predicted confidently that they will succeed.

At a morning press conference -- a daily event now for the once-obscure members leading the open-convention drive -- nine of the House Democrats sat before a iron arc formed by 14 television cameras as Rep. Michael Barnes (Md.) introduced the movement's new leader in show business terminology.

"Today we are able to bring to center stage our leader," Barnes said, "and the rest of us can fade to the background." Barnes then turned the microphone over to Edward Bennett Williams, the famous Washington lawyer and Democratic activist who will chair what is now formally titled "The Committee to Continue the Open Convention."

Williams, president of the Washington Redskins and owner of the Baltimore Orioles, waved his arms like a coach giving a locker-room pep talk and declared with great vigor that his purpose was "to free the delegates . . . to eliminate the possibility of their being held hostage to an oppressive rule."

The lawyer spent most of the session defending himself against reporters' suggestions that he is trying to replace Carter with a new Democratic nominee. Asked specifically about his friendship with Secretary of State Edmund Muskie, one of the Democrats widely mentioned as an alternative choice, Williams said they had dined together a week ago but did not discuss the political situation.

The congressmen present, too, argued strenuously that they are not trying to "dump Carter." When a reporter suggested that the group consisted mainly of Kennedy supporters, Rep. Peter Kostmayer (Pa.) responded, "Personally, I support the president for renomination."

On April 20, however, two days before the Pennsylvania primary, Kostmayer appeared as the featured speaker at a huge Kennedy rally in his congressional district. He did not directly endorse Kennedy, but he gave a rip-roaring speech praising the Massachusetts senator and his brothers.

At yesterday's press conference, Williams belittled a suggestion by Carter's campaign director, Robert Strauss, that opening the convention would lead to "disarray." Williams said he read that statement by his "dear friend" Strauss "with some dismay. . . . I felt I was reading something Brezhnev whispered to his wife under the covers about an upcoming Kremlin convention."

The Carter camp is also worried that disarray will appear on the nation's television screens if there is a major prime-time floor fight in New York over the "open convention" rule. There is certain to be a debate and vote on whether delegates should be bound to honor their earlier pledges, but the Carter backers running the convention have scheduled it for the convention's first day.

In negotiations between the Carter and Kennedy camps, Kennedy's people have tried to have the rules fight scheduled for the evening of the second day, Tuesday, Aug. 12. Last week, it appeared that the Carter camp might give in on that point in return for Kennedy's agreeing to limit the number of platform debates brought to the floor.

In the meeting with Kennedy negotiators this week, however, according to sources in both campaigns, the Carter people said they did not intend to schedule the rules fight for Tuesday night. The matter is still in the air, with more negotiations scheduled.

An open convention was endorsed yesterday by leaders of 35 AFL-CIO unions who said they did not want "programmed robots" choosing the nominee. Several of the endorsers are backers of Kennedy; others have been neutral.

To date, most of the turmoil over "dumping" Carter and opening the convention has been centered in Washington or among Kennedy delegates to the convention. The Post poll indicates that all the hoopla has passed over the heads of the Carter delegates, the people the open-convention advocates have to persuade.

The poll showed that Carter delegates oppose the open-convention rule by 88 to 12 percent, while Kennedy's support it 89 to 11. And it offered an explanation for the Carter backers' firmness: they say they are convinced that Carter can defeat Republican Ronald Reagan in November.