A dispute over President Carter's plans to kill at least 19 major water development projects has opened a serious breach between Congress and the White House that could endanger other parts of the President's program.

Yesterday, the conflict appeared to be intensifying. White House press secretary Jody Powell said the President intends to pursue his attempts to kill any project he deems "an inefficient use of the taxpayers' money." Powell's remarks came a day after the Senate voted 65 to 24 to oppose Carter's plan to review the 19 projects.

Powell made clear that the President will use all lawful means to cut projects once he decides they are based on loose criteria, and that he will seek public support for his position. Otherwise, Powell said, Carter's goal of a balanced budget would be impossible.

However, Senate Majority Leader Robert C. Byrd (D-W.Va.) described the Thursday vote as "a clear signal to the White House that this Congress expects to be consulted (on) matters which come within the responsibility of the legislative branch."

He said this message isn't confined to public works projects but applies to "other things, too." Congress is an equal and independent branch. It wants to be consulted," he said, "not on every little thing, but there are areas on which Congress has a right to be consulted."

He said that while relations between Carter and the congressional leadership are "general good, this was a mistake . . . a serious aberration."

The strong and unexpected Senate floor rebuke to the President was led by Sens. J. Bennett Johnston (D-La.), Edmund S. Muskie (D-Maine), and other Democrats.

It arose in part because flood control, irrigation and municipal water projects are of vital economic benefit to some regions of the country and are dear to the heart of every senator and congressman.

Equally irritating was the way President Carter first made his plans known. For years members have been saying Congress wants prior consultation - a chance to have some input - on major policy decisions. Yet Democratic senators - at an angry caucus with Vice President Mondale Wednesday morning and a meeting with the President Thursday morning - charged that the proposed kills had been sprung upon them without consultation and without even adequate advance notice.

On Wednesday, after listening for a sew moments, former Sen. Mondale smilingly remarked, "Hell, this is not a meeting, this is an ambush," according to several senators who wee present.

One said, "Johnston and Muskie and George McGoven and Gary Hart just got up and raised hell."

One complaint was that most senators first got wind of the proposed kills only three days before they were announced - and then at the end of the week when many were out of town.

John C. Stennis (D-Miss.), a respected and normally very restrained elder, told the caucus that he expected a "general nationwide storm of protest" when the public got more information about what was happening.

McGovern said the proposal to kill the Oahe irrigation project was "the most severe political and economic blow in South Dakota since I came to the Senate."

"Muskie was absolutely livid" about the killing of a project in Maine, said one who was present. "Wendell Ford said, 'We ought to go after these people not with a needle but with an auger.'"

The attack widened into a criticism of White House liaison chief Frank Moore by some senators. Dale Bumpers (Ark.) told Mondale, according to senators present, "He may be able to get a message from the President to the Hill, but he's not very good at carrying messages back." Bumpers asked whether Mondale would be willing to do that, but Mondale turned the question aside and at another point defended Moore, as did John Durkin (N.H.), according to participants.

Next day at the White House, senators complained that the president didn't really understand western water needs, and that McGovern had been assured the Oahe project wasn't listed for axing. Hart told the President the administration "has a credibility gap" because he was twice assured there was no second list of axed irrigation projects, only to learn that the Interior Department had compiled one adding 19 recommended killings to the original 19.

Stennis told the President, "If you've done one thing by this, it's to unify the Congress."

Carter excused the late notification by saying the proposed kills hadn't been decided on until very late and calls went out the same day.

One participant said, "He also told them, 'We're going ahead with this review,' and didn't back up at all. He added, 'I talked about these things in the campaign and it should have been clear I was planning this move.' He also made an allusion to the fact that the people 'are supporting me.'" This was taken by some as a threat to carry the issue to the public over the head of Congress."

What it all adds up to is what Byrd called "a pretty serious spat during the honeymoon period." It could hurt the whole presidential-congressional relationship if not repaired.