Barring significant changes as paper ballots are counted over the next few days, President Carter appears almost certain to win at least a slight majority of the delegates elected at Saturday's straw vote Democratic Party caucuses.

And if the current trend in urban Dade County (Miami) continues, Carter's majority statewide could rise to about 65 percent of the 879 delegates versus 31 percent for the slate supporting a movement to draft Sen. Edward M. Kennedy (D-Mass.) for the Democratic presidential nomination next year.

The size of Carter's majority hinges on Dade County because it has been allocated 188 delegates, more than a fifth of the statewide total.

The greatest ssurprise to participants here was organized labor. There was a heavy labor turnout in many of the 67 county caucuses designed to give the state AFL-CIO leverage in formulating a party platform at the November party convention.

In some counties labor teamed up with Carter slates and in others with draft-Kennedy slates. The labor alliance then tilted the county vote toward whichever candidate it sided with.

Because of this, conclusions about real Kennedy or Carter strength were difficult to draw in many counties.

By this evening, the results in most of the counties were either official or sufficient to show a trend. Carter had won 366 delegates, or 41 percent, and Kennedy 277, or 31 percent. Independent labor delegates, uncommitted delegates and untallied votes accounted for the rest.

The delegates elected Saturday at the sometimes chaotic and unstructured caucuses will join 838 already selected by party leaders for a state party convention Nov. 16 through Nov. 18. There they will cast a purely symbolic straw vote for a presidental candidate. Because most of the 838 are already committed to Carter, a close contest is unlikely at that convention.

It is also unlikely that the November event will draw the press attention that gave such apparent significance to what was universally described as Saturday's "first test of strength between Carter and Kennedy." More reports showed up in Miami to cover the caucuses than there were voters in some of the smaller rural counties.

Statewide, officials guessed that 40,000 registered Democrates -- less than 2 percent of the total -- turned out for what was largely an organizational struggle.

Kennedy's strongest showing yesterday was in Broward County, surrounding Fort Lauderdale. There, Jewish voters upset with the Carter administeration's policies in the Middle East turned out in large numbers to elect 116 Kennedy delegates.

The greatest disappointment for Kennedy organizers was Dade County. Carter holds a 55-vote lead in what was supposed to have been certain Kennedy country. Draft-Kennedy organizers said that they were simply outorganized in this ethnically diverse area.

Carter's most discernible support came from Democrats in the northern areas of the state above Gainesville where the electorate tends to be more Southern in origin and outlook. Carter swept 25 northern counties.

Kennedy won 16 of 28 delegates in what was supposed to have been the Carter stronghold of Orange County, largely because of overlap between the Kennedy and labor slate. The Kennedy turnout in that area around Orlando was determined to be the lowest of the three competing groups but he did well there anyway because of the labor support.

In almost all instances, both Kennedy and Carter organizers said today, delegates who were labor delegates and Kennedy or Carter delegates at the same time were victorious. "Any place that Kennedy and labor were one," said Sergio Bendixen, the Kennedy organization's strategist, "we were victorious."

Similarly, Carter organizers said that alliances with labor saved them from a rout in Palm Beach, where a still incomplete count seemed to be giving most of the delegates to Kennedy.

The overlapping of 34 labor and Carter delegate candidates in Dade County could also prove decisive in assuring a Carter majority statewide should Kennedy forces close the gap in other delegate contests.

Because the 34 have both labor support and Carter campaign support, they are certain to be elected once the paper ballots are counted.

The operating engineers', teachers' and machinists' unions along with the auto workers' union were particularly helpful to Kennedy delegates in some areas. The iron workers, other local of the teachers' and the state AFL-CIO organization itself in Dade County helped Carter.