On this Memorial Day weekend, when Americans mark a ceremony of remembrance that originally honored the dead of the Civil War, there is an effort under way to reopen--or at least to sharpen--the North-South differences within the Democratic Party. Surprisingly, it comes from people closely associated with Jimmy Carter, the first unalloyed southerner to reach the presidency since the Civil War, and the man who liked to say that he had ended the bias against candidates from his region.

Hamilton Jordan, Carter's former political strategist, has been writing and speaking everywhere on the theme that the Democrats need an updated version of "the southern strategy" to have a hope of winning the 1984 presidential race.

In an op-ed article for The Post, Jordan said, "It is not my premise that the southern states are more important than the northeastern or midwestern states. It is my premise that the South will be more difficult for any Democrat to carry in 1984, and consequently deserves . . . early attention."

There is no question that the South will get that attention from the Democratic aspirants; in fact, it already is getting it. Louisiana is likely to have a presidential straw ballot for the 1.4 million people who vote in its gubernatorial election this November. As many as eight southern states will pick delegates as the campaign gets rolling in the third week of next March. So there is no danger of the South's being overlooked.

But Jordan's argument goes beyond tactics and political timing. He says that the Democratic presidential hopefuls should tailor their message to "southern interests and needs--a view of government, economic and defense issues more conservative than the Northeast and Midwest." The reason, Jordan says, is that "if you (Democratic contenders) want to be elected president, you are going to have to carry at least several--and probably five or six-- southern states."

Putting a specific edge on his message, Jordan last week urged his old White House buddy, Walter F. Mondale, to turn down the endorsement of the AFL-CIO, if offered it, because "being labeled 'the labor candidate' will hurt him" in the southern states.

That is not advice Mondale is prepared to take. If he can get the AFL-CIO endorsement, he will grab it. But is he wise? Or does the path to the White House run through Dixie, as Jordan contends?

On the latter question, history is not only on Jordan's side; it reduces his argument to a clich,e. Of the last four Democrats to win the White House, Carter carried 11 of the 13 southern states, Lyndon B. Johnson and John F. Kennedy each carried eight, and Harry S. Truman carried 12. Only Johnson, in his 1964 landslide, could have won without the South.

In 1984, again, the odds are that any successful Democratic presidential coalition will have to include at least the five or six southern states Jordan sets as a minimum. But will those states be harder to win than a similar block in any other region, as he contends?

Maybe--and maybe not. A series of Washington Post-ABC News trial heat polls pitting Reagan against Mondale and Sen. John Glenn show that the only region where Reagan consistently runs ahead of his national pace is the West. The South tracks closely with the East and Midwest. In the mid-May poll, for example, Reagan led Mondale by three points in the South and four in the Midwest and trailed by four in the East. He trailed Glenn by four points in the South, six in the Midwest and eight in the East. Those are not large differences.

Both history and common sense support the polling evidence that, as the South has more and more come to resemble other sections in its economic and demographic mix, it has tended to swing with--and not against--national political currents.

In 1980, even with a consciously southern president at the head of the ticket, the Democrats were routed in the South. In 1982, they came back as strongly in the South as in any section. The key to the Democratic victories in the South--as elsewhere--has been the mobilization and expansion of a low- and middle-income voter coalition, including increasing numbers of blacks and Hispanics. That is a strategy based on economic, social and educational issues, which are national in scope but have particular saliency in the South. It is not a strategy that pits the South against the North --or labor against other elements of the Democratic coalition.

The AFL-CIO not only supports this kind of vote mobilization effort, but also it consistently pushes the economic issues on which such a coalition rests. That is why AFL-CIO president Lane Kirkland gently rejected Jordan's contention, reminding Carter's former campaign manager that Carter had told labor in 1976 that he "could not have been elected without your endorsement and your support."

Kirkland did it gently, because that is the way he was reared. In Camden, S.C., suh!