It was not without a sense of satisfaction that President Carter's man in south Florida, Chuck Parrish, sat back to listen as the all-news radio began to announce the fruits of his behind-the-scenes labor.

For weeks, in the name of the president, Parrish had been forced to apply heavy pressure -- not upon recalcitrant local politicians (although they seem to thrive even better than oranges here) but upon the Carter White House, which was about to commit political harakiri over the issue that has come to dominate the presidential election to this battleground state.

The white House was on the verge of setting up a new processing center for Cuban refugees in the middle of a middle-class neighorhood of south Floridians who have had it right up to their ballot boxes with the refugee problem -- and with the president who happened to be in office when the problem exploded upon them.

Florida's Gov. Robert Graham had been leading a chorus of prominent officials who opposed the plan, still officially a secret, to establish a new refugee center in the state. And in the wings, Parrish was orchestrating the chorus, knowing that the polls were showing that the refugee issue had come to overshadow all other in the struggle to win the electoral votes in the most populous of the states and had made up Carter's 1976 southern base.

Presidential politicking had come to a near halt, as the governor, Parrish and others urged that Carter made no visit to the state until the rufugees problem was solved.

Finally, Parrish received assurances that his battle was won ans so it was that he was listening with satisfaction as the radio announcer begin to say that there would be a new processing center for refugees from Cuba . . . that the center would be located in Puerto Rico . . . and that the center would serve all refugees except those destined for the Miami area.

Wait a minute! Except the Miami area?

Chuck Parrish starred at his radio in disbelief. and then, he recalls, he did the only rational thing that a reasonable man could do in such circumstance: "I went straight through the ceiling."

For what seemed like an hour, politics went into a state of suspended animation in the Carter-Mondale offices in Miami, until the all-news radio station announced its correction: Miami's refugees would be processed in Puerto Rico, too. And in the Carter Mondale offices, located in Miami's Little Havana, hearts were started once more and the politics of reelecting the president resumed.

Democratic politicians in the state agree that the resolution of the refugee problem -- or at least a tangible and demonstrable beginning at resolving it -- was crucial to Carter's chances for carrying the state. Earlier this month, a poll by four state newspapers showed Carter and Reagan even at 38 percent with independent John B. Anderson a distant third with just 8 percent.

Since then, a number of prominent Democrats, among them the governor, figure that Reagan has regained the lead. Moreover, as Graham said in a recent interview, there were other statistics in that poll that indicate significant problems for Carter in the state.

"The biggest surprise in that newspaper poll was that the president was actually trailing Reagan in south Florida," Said Graham, who gave the nominating speech for the president at the Democratic National Convention. "That is an area in which the president needs to do well."

Ronald Reagan's Florida coordinator, Herb Harmon, figures that Reagan and Carter will divide votes fairly evenly in the center and south of Florida. If this is the case, Harmon says, the question of who wins Florida's 17 electoral votes will be decided in the small towns and rural north part of the state and in the Florida panhandle -- area that were once the core of the George Wallace vote in this state.

The latest newspaper poll showed Carter with the edge among these voters, many of whom feel strong ties to the deep South and especially Georgia. But the Reagan camp comforts itself by recalling that these voters are philosophically more in tune with Reagan's conservatism than they are with Carter's less definable political philosophy.

Built into Reagan's strategy is a concession that Reagan will receive no more than 45 percent of the vote in Dade County (Miami). Yet a number of state Democrats concede that Reagan may do better than that, because of a series of dissatisfactions among Dade voters that spring from the refugee problem.

In 1976, the 92,000 votes Carter received in Dade County amounted to well over half of the 166,000-vote margin by which Carter defeated Gerald R. Ford in the state. But this year the uncertain politics of the refugee problem underlies significant problems that Carter faces in Dade County.

Feeling in Dade have turned bitter, and even mean, as a result of the influx of 118,000 refugees from Cuba since April, an estimated 60,000 of whom will apparently remain in the Greater Miami area.

The refugee problem in Dade has set white against Cuban, black against Cuban, black against white, and in a sense, all of the above against Carter.

"The refugee problem has almost made people racist again." says one Carter Democrat in the state. And Gov. Graham observed:

"It's sad. Up until six months ago, there was a good feeling among the people, as good or better as there had been at any time in the last 20 years."

A recent statewide poll showed that 23 percent of those responding felt that the immigration question was the most important issue affecting their lives -- more so than the economy or any other issue that rates highly in polls elsewhere. "The refugee issue has become symbolic," Graham said. "It stands for frustrations over the rate of inflation and unemployment and crime." s

The crime rate has soared in Dade County, and police officials have been widely quoted as attributing much off the increase to the lower class and even criminal elements among the refugees that Cuban President Fidel tro has dispatched to the United States this year.

Miami has declared itself officially a bilingual city, and the prospect of a conversion to bilingual education has become a matter of intense public controversy in the county.

Longtime residents complained that everyday life changed markedly because of the influx of refugees; even renewing a driver's license has become an all-day procedure, they complain. And for visitors in downtown hotels such as the plush new Omni, English is now the number two language and getting an accurate telephone message or ordering a meal becomes a chancy procedure.

Anit-refugees feelings run measurably high. The Miami Herald recently asked its readers whether the new wave of Cuban immigrants would have a positive or negative effect on the area. Seventeen percent of whites responding said the effect would be positive, 68 percent said negative. Among blacks, 16 percent answered positive, 57 percent negative.

In contrast, when questioned about previous large immigrations of Cuban refugees, 50 percent of the white's thought the effect would be positive and 29 percent thought it would be negative, and 48 percent of the blacks said positive while 45 percent said negative.

At least 116,000 of Dade's 674,000 registered voters are Hispanic, according to Democratic Party calculations. Most of these are Cuban refugees, and most of those Cuban refugees vote a staunch conservative Republican line.

Another 108,000 are black -- they will vote overwhelmingly for Carter. But Democratic officials say they are concerned that the 1980 voter turnout of blacks in riot-torn Dade County may fall far short of the more than 70 percent turnout 1976.

Local officials have made Carter a frequent target of criticism as the administration seesawed through its search for a refugee police. The plan that had substantial support within the White House -- to create a new refugee processing center on an old naval blimp base in Dade's Richmond Heights area -- would have made political matters even worse.

"It would have been a disaster," Graham said.

"The scale of the plan indicated that the government would be prepared to accept large numbers of refugees on a more or less permanent basis," Graham said. "It would not have sent the message that the president needed to send to the voters of this state."

With the center now planned for Puerto Rico, a politically proper message has been sent to Florida's voters, Graham believes. The administration also has agreed to support legislation to reimburse state and local governments for refugee relocation, and is moving to close by the end of this month the squalid Tent City refugee site under a Miami expressway.

The demands of the local officials have mostly been met, but the bitterness in south Florida remains. It presents a difficult backdrop for a presidential campaign -- especially for Carter, who had one major problem in the area even before the latest refugee crisis. He evoked more emnity than enthusiasm among one prominent bloc of Democratic voters: the Jews.

On the stage of the overwhelmingly Jewish Point East condominium in North Miami Beach, Sen. Henry M. Jackson (D-Wash.) began his pitch for the reelection of his embattled colleague, Sen. Richard Stone of Florida, with a cool, obligatory plug for another man for whom he feels little personal or political affection.

"I supported President Carter after . . . [the 1976] election and I'm supporting him again this time" -- a chorus of boos erupted from the more than 1,000 Jewish senior citizens in the audience today. Jackson, normally the hero-politico of this crowd, looked momentarily startled and then quickly understood. He went on to extol the virtues of Stone, and Carter was mentioned no more.

Later, one who joined in the booing, Saul Levy, who is now 66 and transplanted from Long Island, N.Y., where he was in textiles, explained: "Carter's been anti-Jewish. I've been a Democrat all my life. But now for the first time I will not vote for the Democrat."

The latest newspaper poll showed Carter with 34 percent of the Jews, Reagan 18, Anderson 17, and a huge 31 percent undecided.

In a sense, Carter's fate in Florida could be linked to his ability to turn out large numbers of Jewish votes on Nov. 4; and that in turn may be linked to Stone's fate in his Senate runoff next week. According to state pols and polls, Stone, who is Jewish is trailing Florida's insurance commissioner, Bill Gunter.

If Stone is not on the ballot in November, it may be very difficult for the Carter organization to turn out the margin they need among Jewish voters.

""It will be terrible, terrible," says Annie Ackerman, who has parlayed an ability to organize the politics of the Point East condominium into a reputation among all who have ever practiced presidential politics in this state. ". . . There is no enthusiasm for Jimmy Carter among the Jews. We'll have to whip it up. But without Stone on the ballot, I'd hate to think about it."