With a partisan promise from Sen. Edward M. Kennedy that "our day is coming again," Democrats wound up their national midterm party conference today and set out to fight the Republicans on the issues of economic, social and foreign policy they think will bring them victory in November.

Kennedy's widely anticipated address, the highlight of the weekend meeting's final session, solidified his reputation as the Democrats' most accomplished orator and did nothing to damage his status as the front-runner for the 1984 nomination.

The Massachusetts senator was interrupted by cheers and applause almost 60 times in 35 minutes, as he catalogued the issues from women's rights and Social Security to the environment and the nuclear weapons freeze that the conference policy statements laid down as the basis for the coming campaign.

Emphasizing the unity that conference planners tried to show at every turn, Kennedy, whose campaign against President Carter was launched at the mini-convention of 1978, said that "no matter what side you were on in the primaries of 1980 . . . the enduring principles that now unite us as Democrats are stronger than any political differences that may ever divide us again."

While five other presidential hopefuls shared Friday's opening session and one--former Florida governor Reubin Askew--chose not to speak at all, Kennedy waited until the mini-convention's final hours to make his speech.

His cheers probably eclipsed those for former vice president Walter F. Mondale, the unofficial winner over Sens. Alan Cranston of California, John Glenn of Ohio, Gary Hart of Colorado and Ernest F. Hollings of South Carolina on Friday.

But most observers thought the setting and reaction were less emotional than in Memphis in 1978 or Madison Square Garden in 1980, when Kennedy began and ended his challenge to Carter. And, by most estimates, Mondale came away from the weekend a stronger--not a weaker--opponent for Kennedy.

Ironically, Kennedy gained one of his longest ovations by praising his erstwhile rival, Carter, a man whose name was barely mentioned by earlier speakers.

"I had my disagreements with the last administration," he said. "But on the vital issue of human rights, Ronald Reagan is wrong--and Jimmy Carter was right."

Kennedy's midday speech closed the conference, as far as most of the nearly 900 delegates were concerned, and they streamed out of town, leaving just a corporal's guard to give formal ratification to the reports from Saturday's seven issues workshops.

The statements on domestic and foreign policy adopted there--and especially the indictments of administration actions in these areas--will be echoed by hundreds of Democratic candidates this fall.

Party chairman Charles T. Manatt designed the session--mandated by the 1980 convention--as a campaign kickoff, filling the delegate seats with party and elected officials and focusing the agenda on what he and others regard as weak points in President Reagan's record.

Manatt said the session had been "excellent" for its designed purpose. "We come out with the spirit and unity we need" for the 1982 campaign, he said.

Officials were particularly pleased that the large contingent of House and Senate members thought the policy positions would be of help--and not an embarrassment--in their own races.

Before Kennedy gave them the applause lines that dozens of other candidates' speechwriters will probably borrow, with or without credit, two Democratic congressional leaders tried to deal with the charge that their party failed its responsibility as the opposition by acquiescing in Reagan's programs and not providing alternatives of its own.

The answer, said Senate Minority Leader Robert C. Byrd of West Virginia and House Majority Leader James C. Wright Jr. of Texas, is simply to elect more Democrats.

"Five votes," Byrd said. "Five more Democratic senators. That's all it will take to shift control of the Senate from those who tear down to those who build."

In the House, where Democrats have a 51-seat majority, Wright maintained that "the change of a dozen votes or less would have given us a working Democratic majority" that he said would have stopped the "savage butchery" of the Reagan budget.

Neither man referred to the numerous defections of Democratic lawmakers that helped Reagan pass his programs in 1981.

Kennedy, who voted against all the Reagan policies, said with a touch of self-satisfaction that "the struggle last year sometimes seemed lonely . . . . We were advised to be cautious and callous and uncommitted. We were told to quiet our voices, to lower our vision, and to trim our convictions to fit a reactionary time. We were warned to say very little and to stand for even less.

"But that is not the kind of senator I have sought to be or the kind of Democratic Party you and I have fought for," he said. "And events since then have reaffirmed a vital truth: The last thing this nation needs is two Republican parties."

While much of the energy and talk this weekend went into developing policy statements designed to answer the complaint that Democrats have no new ideas, Kennedy played traditionalist. "Rethinking our ideas must never be an excuse for retreating from our ideals," he said.

Invoking a litany of causes like education, welfare, health and social justice, Kennedy said that Democrats "do not have to call ourselves neo-liberals or cozy up to neo-conservatives" to prevail in the 1980s.

"We can be true Democrats without becoming either the party of the bleeding heart or the party whose heart has turned to stone," he said.