When President Carter was asked last month about what the reporter called "the widening schism in the Democratic Party between yourself and Sen. Kennedy," he rejected the description out of hand and called the differences between himself and the Massachusetts Democrat "very minor."

In one respect at least, the president was wrong. Edward M. Kennedy leads Carter in polls of Democratic voters for the party's 1980 nomination by a margin that no one would call "minor." The most recent survey, taken by the Los Angeles Times in December, put the margin at 58 to 35 percent nationally in Kennedy's favor.

Patrick Caddell, the president's pollster, dismisses such trial-heat polls as "abstractions," nothing that Kennedy would stir more conflicting emotions as a flesh-and-blood challenger than simply as a name on a pollster's questionnaire.

Hamilton Jordan, who is framing Carter's reelection strategy, says brusquely that "I always assume we'll have tough competition," and says he worries more about the "factors we can conrtol."

Mark Siegel, who was Jordan's deputy and Caddell's friend until policy differences led him to quit the White House last year, says Carter is "governing in such a way as to alienate the key elements of the Democratic Party coalition and force them, despite their own differences, to seek an alternative."

That alternative, Siegel says, is Kennedy -- and he hopes that when the time is right, Kennedy will be there "to lead the party where I think it wants to go."

Whether he will be or not is a matter of endless speculation and debate. Kennedy himself says no, and his close friend, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who has been publicly skeptical of the senator's disclaimers at time in the past, this time says, "I believe him."

Whether or not Kennedy runs, there is no questoin that the divisions within the Democratic Party now loom as a major challenge to its ability to govern successfully in the next two years and extend its control of the White House beyond 1980.

Those divisions center mainly on the domestic economies Carter will seek in the budget he sends to Congress next week, and the doubts many influential Democrats harbor on whether his basic economic strategy will curb inflation without triggering a recession. .tBut they also extend to the principal international issues Carter plans to bring before Congress -- a strategic arms limitation treaty with the Soviet Union, the normalization of relations with China and a new mulilateral trade agreement.

Ken Young, the new chief lobbyist for the AFL-CIO, notes ruefully that when "I came into the legislative department in the 89th Congress," following Lyndon B. Johnson's 1964 landslide, "I couldn't figure out why they were paying me. All we did was help the president get his program through -- and it wasn't that hard."

"Now," he says, "on all of those major issues, we will be in opposition to a Democratic president -- and it's a helluva lot harder. We've never been in this position before."

The position of the labor federation is unique in more than one sense. Almost alone among the major interest groups, it is linked both to constituencies of the left that are in dissent from Carter's economics and to constituencies of the right that oppose key elements of his international policy.

That seems puzzling, until one remembers that the AFL-CIO's leadership, starting with 84-year-old president George Meany, is probably the oldest of any element in the Democratic coalition. They are naturally resistant to the transition Carter and many others see taking place within the party.

The federation leaders grew up in a Democratic Party that was interventionist abroad and expansionist at home -- or, as they would put it, as committed to the defense of freedom in the world as to the pursuit of justice in America.

They find much in common, therefore, with those who see elements of apostasy in both the foreign and domestic policy of the Carter administration.

Sen. Daniel P. Moynihan (N.Y.) says that he and Sen. Henry M. Jackson (Wash.), two of the Democrats closest to Meany and the federation, share a view about Carter's fundamental error:

"He has a right wing domestic policy and a left-wing foreign policy, and that's sure way to lose an election."

Judging from the volume of dissent on both wings of the party, that would seem to be a near certainty. But the appearance is almost surely misleading. Much of the local complaint comes from those who are resisting the tides of change Carter and his aides see sweeping America and their party. And many of the Democrats who are part of that change think it is the critics -- not Carter -- who misread the situation.

If one listens carefully, a strong sense of historical displacement is heard in the criticisms of Carter's policies.

Moynihan, for example, declares flatly that "in foreign policy, there are two Democratic parties, with a well-defined structure and an organizational history of their own." Those "parties" clashed bitterly in the Vietnam debates of election year 1968 and 1972 and never have reconciled their fundamental differences on the larger question of America's response to communist and third-word challenges.

Moynihan, a traditionalist hardliner, says he has told the Carter administration tht "when it came time to appoint your side was named, refer to us as their enemies."

"In the SALT debate," the senator added, "we are going to make them realize we exist. There is no point in having people who think of Sen. Jackson and George Meany and me as dangerous men ask us to pass their SALT treaty. They didn't want our views inside their government, but by God, they're going to hear them from outside."

While Meany stands with Moynihan and Jackson or SALT, he also stands with other older-generation democrats who dissent, for quite different reasons, from Carter's domestic and economic policies. Meany says those policies are "more conservative than Calvin Coolidge's."

Again, the theme of the criticism is that Carter has abandoned the true faith in which these Democrats were raised.

Americans for Deocratic Action, founded more than 30 years ago by Hubert H. Humphrey and his friends as an anti-communist liberal movement, gives Carter "failing grades."

Douglas Fraser, president of the United Auto Workers, said at the Memphis mini convention: "We are told that times are charging and we must change with the times. I hope the Democratic Party never changes in its commidtment to those who are most in need of a helping hand from their government."

And Rep. Parren Mitchell (D-Md.), chairman of the Congressional Black Caucus, says, "These are not 'different times' for senior citizens whose only hot meal each day comes from the government. It's not a different time for the blacks who are still unemployed."

It is such people as these who see political disaster in Carter's approach to budgetary and economic policy.

Members of the National Advisory Committee for Women, in the statement that led Carter to ouset Bella S. Abzug as its co-chairwoman, complained that his budget and inflation policies both represent "an unacceptable attack on the already low economic status of American Women."

Amid so much dissent, clearly the possibility of an intra-party challenge to Carter Exists, and California Gov. Edmund G. (Jerry) Brown Jr., for one, appears eager to give it a try. But Brown is dismissed as "no improvement over Carter" by both George Meany and George McGovern. He has failed to identify with those who are either left of Carter on domestic issues or to his right on international issuees. And Brown, unlike Kennedy, badly lags Carter in the polls.

Kennedy is the hope of many of the dissenters, but one who is openly urging his candidacy, Machinists Union president William Winpisinger, admits he finds the senator "very standoffish." Many admirers think this is not Kennedy's time.

"In some ironic respects," observes Sen. Gary Hart (D-Colo.), "I think Ted Kennedy reflects the last throes of the New Deal" of the 1930s. "He still has the conviction of the efficacy of public programs to meet public needs, and his main issue, health care, is really the last item left unfinished on the New Deal agenda."

"That's not at all bad in itself," Hart says, "but I'm not sure this is the time for it."

Talking to Kennedy, one gets the sense that he is not altogether happy at being called the last New Dealer and not altogether certain thta Carter is wrong in saying that times have changed.

His public rhetoric is full or ringing challenges to the political fates. At the Black Cause dinner last September, he declared: "Some slay that a different tide is running in this country now. They say the Bakke case and Proposition 13 are the wave of the future. They tell us to slow down, to take a rest, to let things be. But I am here tonight to tell you that they are wrong."

And in his wildly cheered speech at the Memphis mini-convention, he declared: "Sometimes a party must sail against the wind."

But in an interview last week, Kennedy sounded as if he had trimmed his sails. He said he:

Agrees that "the message of the voters" is to "end fraud and waste" in government programs and has scheduled his first hearing of the year on exactly that problem in the health programs.

Believes "the central question of our time is certainly inflation," and "I intend to support the administration" program of wage-price guidelines and "a significant reduction in the deficit."

Still disagrees with the energy and tax bills Carter signed, but says that in those areas, as in others, My principal areas of difference have been more... with the actions by the Congress... than the administration's initiatives,"

That last is a fundamental point, because, as Rep. David Obey (D-Wis.) says, "It is a mistake to think that Jimmy Carter is more conservative than the Democrats in Congress. He's not. This is a lot different place than four years ago, and a lot of people think those old programs aren't working any more."

Congress has undergone a generational change in membership, and is dominated now by younger Democrats who pride themselves on being closely attuned to their districts. Partly for that reason, House Majority Leader Jim Wright (Tex.) predicts that whatever Carter recommends in budget cuts, "the tendency here will ve to do him one better." And partly for that same reason, there is widespread skepticism among liberal Democrats about Kennedy's Memphis statement that Carter's proposed budget cuts could tear the party apart as much as did the Vietnam war.

Kennedy himself says his anxieties were at least partially relieved by "the significant restoraton of funds" -- reportedly totalling $2 billion -- carter ordered just before Christmas. And his old friend, Tip O'Neill, says of the possibility of a serious party split on budget issues, "I don't believe that at all."

Where Kennedy is supported is in his contention that Carter will be challenged if he tries, as expected, to push up mititary spending while cutting back domestic programs.

Influential House Budget Committee member Obey says, "If he really proposes that kind of defense budget, he's going to have a lot of people walking away from him. If he made a stupid commitment at NATO" -- to increase defense spending 3 percent a year above inflation -- "he should say it was stupid and forget it."

For Carter to abandon that commitment would, of course, increase the criticism from the Moynihans and Jacksons and Meanys on the other end of the Democratic spectrum -- as well as have an effedt on America's European Allies.

But Majodrity Leader Wright, no critic of the Pentagon himself, says "there will have to be some token cuts, at least, in defense by the budget committees, and he will just have to recognize that as a reality."

Wright also voices publicly what many other Democrats only hint -- a fear that Carter's budget and economic policies run much greater risk of bringing on a recession than the White House concedes.

"The only thing that could put us into a real dilemma as Democrats," Wright says, "is if these damn high interest rates spin us us into a recession. I'm scared to death they're going to do that, and it could be just devastating, because we won't be able to reduce the deficit any way in a declining economy, and we'll have inflation and uneploment to boot."

That nightmare scenario is predicted by some Democratic Economists outside the administration, but Tip O'Neill says that if the economy slumps, "I am not going to allow people to go to bed hungry for an austerity program. No way. If unemployment goes up to 6.5 percent and I hear nothing from the White House, I'll be calling the committees to come-forward with an economic stimulus and public works program of our own, and we'll put it on his desk."

Sen. McGovern, for one, believes that a recession will increase the likelihood of an intraparty challenge to Carter.

But Caddell, the president's pollster, notes that each passing month makes it harder for anyone to organize such an effort. And he points out that many of the liberal activists who might lead such a campaign are otherwise occupied. They are employed by Jimmy Carter in running his administration.

As for the liberal critics who are still outside, Hamilton Jordan, the president's chief political strategist, dismisses them as "the people who opposed Jimmy Carter's nomination in the first place. At the practical level, the party has adjusted to the new mood in the country, and they know Carter is attuned to that mood."

The one threat the Carterites do not entirely dismiss is that of apathy. Election-day turnouts among hardcore Democratic voters, especially from the minority and low-income groups, have been declining in recent years. And the activists might sit on the sidelines in 1980 because of disenchantment with Carter.

"If they continue to follow the present policies," says the AFL-CLO's Young, "they will have tremendous difficulties getting the traditional constituencies to the polls, no matter what outside organizations like ours do. If the debate is to be on who is most 'fiscally responsible' in cutting back social programs, why would an inner-city black or a labor guy vote?"

Some suggest that Carter knows this and will crank up the economy, the budget and the legislative program again next year. But Vice President Mondale says otherwise.

"I think we have to stay the course," he says. "There really is no alternative but to get this inflation rate down."

Jordan sees it the same way. "We live in a non-ideological period in our history, when the American people are more interested in seeing some problems resolved than in seeing some partisan philosophy applied across the board."

Jordan sees a significant gain in polls showing that a plurality of voters think Democrats will do a better job than Republicans in reducing government waste and cutting taxes. Others in the White House find similar encouragement for the party in greater voting unity between southern and northern Democrats in Congress since Carter became president.

But one of Carter's most consistent backers in Congress sees great risk in that kind of cool, calculating strategy. "Carter's problem," says Rep. Obey, "is that he appeals to people strictly from the nose up. He never gets to their heart, or their guts. People don't know what makes him amd -- except inefficiency. Unless a politician reveals more of his emotional makeup to people, his hold on them is bond to be thin. And his is really thin."

That argument is not totally rejected by the Carterites.

Presidential assistant Anne Wexler says, "I would hope that the president can motivate people to get involved in 1980, but I don't know if it's going to happen. I think that if Teddy ran in 1980, or when he runs, whenever it is, I would think he can probably motivate more people to vote than Carter does."

Caddell hints at a careful strategy of gradually defusing the opposition to Carter's renomination and reelection, rather than trying to build a massive groundswell of positive support for a president who plainly engenders no such emotion.

"Circumstances," Caddell says, "have made it harder to hold tightly together the constituencies in our own party. But they have made it easier to win the general election. Intense support breeds intense opposition. What we have here is a blanket that suffocates those fires."

Perhaps for that reason, the analogy suggested by both Rep. Morris Udall (Ariz.), Carter's most persistent liberal challenger for the 1976 nomination, and Rep. Jim Jones (Okla.) is that Carter may eventually be seen as an Eisenhower-like figure in the history of his party, one who gave it the White House for eight years but did little to set tis future direction.

"I'm sure," says Jones, an emerging force in the party's conservative wing, "he'd like to be much more of an activist, but he's being cast in the role of an Eisenhower. He'd like to make bold moves, but he's very good politician and he knows it's not possible."

Udall observes of the man who defeated him for the nomination: "I don't think he has any plan to leave a rebuilt or a reborn party. He just wants to be as good a president as he can for the next six years. He's more like Ike than FDR, who built a coalition that outlived him. I don't see Carter doing that."

"Eisenhower, you remember, never did much to reconstruct the Republican Party," Udall says, "and by the time he was gone, the Goldwater and Rockefeller folks were at the gates, ready to fight for control. By the time Carter is gone, our old coalitions may re-emerge and contest for control. But until then, it's his"

And the final word on the subject belongs to Anne Wexler: "I think that Carter has a vision of the country that is very accurate. I don't think he articulates it nearly as well as he could, but I think it's in his head.... He's a planner, and he takes the long view, and he's essentially trying to create a stable society. That may not be very exciting, but if I had to choose between that and a lot of other things for my children; I certainly think that's a place to begin."