"Have You Lost All the Love You Had for Me?" sang country singer, fiddler and Senate majority leader Sen. Robert Byrd (D-W.Va.) near the end of last night's $1,000-a-plate fund-raiser for the Democratic National Committee.

Was he fiddling while the party burned? Apparently not. Nobody in last night's crowd seemed to have lost any love for President Jimmy Carter. The song was pointedly dedicated to "all the Democrats who are running for re-election," and to make it even more clear, Byrd dedicated his next number to the man he said "will still be our president after the next election."

The theme of the evening was party unity, which has seemed shaky in recent weeks. Last night more than 1,000 hard-core Democrats made it clear that for now Jimmy Carter was at the center of that unity. The president received a long, loud standing ovation when he was introduced by Gov. James B. Hunt Jr. of North Carolina as "a man that even the Republicans believe is one of the best presidents in history."

Earlier, to similar applause, Hunt had said, "We can be proud of the job President Carter has done for this nation. He has restored dignity and compassion to the White House."

The name of Sen. Edward M. Kennedy (D-Mass.), who is being pushed as Carter's rival for the Democratic nomination next year, was not mentioned from the podium during the entire evening.

Kennedy had appeared briefly, earlier in the evening, and was mobbed by the usual horde of admirers -- mostly media people. Walking through the receiving line shaking hands, he looked like the center of a slow-moving football scrimmage. A halo of light engulfed him, and moved with him, formed by the portable lights of a small knot of television cameras recording the scene.

More than a score of reporters, only inches away from the senator, kept pace, trampling some of the paying customers. A fistfight nearly broke out between one guest in black tie and a television cameraman in more casual garb.

"This doesn't make any sense," Kennedy said to a huddle of his aides.

"This makes no sense at all," an aide confirmed. "You can't work the crowd in there."

"How do real people deal with this situation," asked Tom Southwick, Kennedy's press secretary, as the senator was whisked away in a beige sedan.

The crowd was called "grass roots" by Hunt and "of the people" by House Speaker Thomas p. ("Tip") O'Neill, yet most of the formally clad guests looked as though they had never seen a grass root in their lives.

But they had seen years of Democratic Party politics, and their first loyalty, clearly, was to the party. As for the individuals they support, according to lawyer J.D. Williams, "they vary. Ray Marshall is for Carter and Charlie over there is for Carter. The rest of the crowd could go either way."

"A very hot item, Kennedy," said Pat O'Connor, chairman of the Democratic House and Senate Council. "But this is still a Carter-Mondale crowd here."

Judging from the comments Carter got during a half-hour of hand-shaking, O'Connor was right.

"I think you're doing a wonderful job," one woman told the grinning President.

"He's cute. I love him," said Sarah Baum, a Memphis high school teacher.

Carter's grin got even wider when he was introduced to three attractive young women from Georgia. "Wow," said the president, "I think I'll just stay here. Just beautiful."

To Maine attorney Harold Friedman, the evening was "like the Ringling Brothers-Barnum & Bailey Circus." Watching it, he swore that he would never go into politics. "I'm going back to Maine to try my cases and go fishing," he said.

Predictably, there were no Republicans in sight. But among the Democrats, lots of stars came out. Like:

Most of the cabinet members; White House Hamilton Jordan, Sarah Weddington, Anne Wexler, Frank Moore and Kit Dobelle; Mideast negotiator Robert Strauss; Office of Management and Budget Director James McIntyre; lots of visible senators like Frank Church from Idaho and Howard Metzenbaum from Ohio, even larger numbers of representatives; a whole herd of governors and tables and tables of out-of-town Democrats. And Vice President Walter Mondale, who was whispering something probably very interesting to Church when a reporter stuck a nose into the conversation.

Mondale immediately stopped whispering, threw an arm around Church and said, "I think you're just the best senator I've ever seen."

Earlier, in a brief exchange with the media, Sen. Kennedy was still talking hypothetically about what he would do "were I to be a candidate."

In such a situation, he said, "I would talk about the issues that are most on the minds of the American people."

The issues, he said, include "the state of the economy, the rate of inflation, and the issue of energy. These will be the subject of important debate and discussion next year in the country and in the Congress. These are things I intend to talk about and I think he [Carter] will, too." Asked whether he thought presidential leadership would be a legitimate issue, he replied simply, "Yes."

Of the letter President Carter had sent him earlier in the day, Sen. Kennedy said, "I'm glad to get his letters, and I am sure he is glad to get mine." He said that he had looked at the letter "only briefly on the way over," and that it had included "a transcript of the events of last evening, most of which I had already seen on television." Asked whether he had any response to the letter, he said, "I don't think it needs a response, really."

The "events of last evening" to which Kennedy referred were remarks Carter made in Queens, in which he referred to his own steadiness during crisis and said he did not panic. Some interpreted that as an indirect reference to Kennedy's actions at Chappaquiddick 10 years ago.

Later, President Carter was asked whether the letter was an apology to Kennedy. "It was a condemnation of the media distortion of what I said" Carter answered.

Carter's formal address was sprinkled liberally with two elements: superlatives about the Democratic Party and appeals for party unity. He also inserted strong plugs for two pet programs that have been having trouble in Congress, SALT II and the energy program. "The members of Congress do give me great support -- the last two days," he said wryly. "Last week was one of those weeks that's just best to forget."

"A united Democratic party" was a phrase that kept coming back as a refrain as he listed the party's accomplishments from the Depression to the present, and it was reinforced by repeated variations on such words as "unity" and "together."

He carefully avoided pushing his own candidacy for re-election, but, with an audience heavily loaded with members of Congress, he did not resist such lobbying points as, "We must not play politics with nuclear arsenals."

The closest he came to his own political problems may have been in a reference to defects in the SALT agreement and an oblique allusion to his standing in opinion polls.

"I could have written a better SALT treaty, had I done it unilaterally without consulting the Soviets," he said, pleading for a recognition of the practical compromises involved.

And in a direct appeal to members of Congress, he suggested, "You know that your constitutents love you as an individual, but they think poorly of the institution of which you are a member."

But most of the speech was a plea to "focuss on the issues that unite us."

"With selfish divisions among ourselves," he said, "our voice is fractured and cannot be heard."

But perhaps the clearest statement of the evening's mood was made by Governor Hunt, who titillated the crowd in his introduction of Carter by saying that he would break the evening's rule against references to personalities and then went on to a perfectly safe assault on Republican personalities.

"I'll tell you why I'm here with my delegation from North Carolina," he said. "We don't want John Connally or Ronald Reagan in the White House."