Southern governors agree that Jimmy Carter again would sweep his native region if the presidential election were held today, but concede the former Georgia governor's support is much softer than in 1976 when Dixie voters provided the margin that swept him into office.

Virtually all the pro-Carter sentiment, however, came with reservations from either the 11 out of 18 Southern governors gathered here for their annual conference or their top aides. Additionally, there were predictions that the president faces a tough fight from Republican Ronald Reagan in Florida, Texas, Virginia, Mississippi and Tennessee.

"There is a frustration because we have certain (economic) problems," said Mississippi Gov. William Winter, a Democrat who conceded that Reagan is leading Carter in his state. Winter said he expected increasing Democratic momentum would carry Carter to victory there.

John Reid, press secretary to Oklahoma Gov. George Nigh, would only shrug when asked about his Democratic boss' public predictions of a Carter victory. "Sure they're all talking Carter," said Reid, jerking a thumb toward the eight Democratic chief executives here. "But if they're anything like our state -- well, they've written off Oklahoma. "There's no point (for Carter) even campaigning there."

Democratic Gov. Bob Graham said Carter's main problem in Florida is the thousands of Cuban and Haitian refugees that have been stranded in the state. "If Carter does not deal more effectively with the refugee question than he has in the last 150 days, it will hurt him," says Graham, who delivered Carter's nominating speech at the New York convention.

Graham said residents of his politically important state are eager to see more federal support for refugee services, as well as strong defense policies in the Caribbean region. What's more, Graham said, the president has been hurt by his refusal to participate in the first presidential debate along with Independent candidate John Anderson. "I would candidly say that the net effect of not being in Baltimore with Reagan will have to be negative on the president," said Graham.

Significant by his absence is Texas Gov. William P. Clements Jr., a Republican who has been loudly critical of Carter and is being credited with rallying a staunch Reagan vote in his home state that is threatening Carter's 1976 victory record there. Clements sent word that a bout of flu had kept him at home, but some skeptics here wondered whether the governor's work on a Tuesday Reagan fund-raiser had not had more to do with his decision to stay away.

"Texas has always been strong Reagan country," said one Clements aide. "And Reagan's got three of the most powerful politicians in the state out stumping for him -- Clements, (former Gov. John) Connally and (former U.S. ambassador to Britain Anne) Armstrong. If that won't do it, I don't know what will."

Most of the seven Democratic governors in attendance here readily acknowledge that Carter has been less popular in the South than they had hoped, and they cited current economic and energy problems as the primary reasons. But they said voters in their states are beginning to realize that difficult problems engender painful solutions, and that such actions may be necessary even when it won't win friends for the president.

"Now, upon more sober reflection there is the realization that nobody has the capacity to provide all those solutions, said Mississippi's Winter. "So we're seeing a determination, in the South, to stay with a man who understands our own special problems."

Reagan's Labor Day remark linking the Ku Klux Klan to Tuscumbia, Ala., cost him votes in Mississippi, where, Winter said, voters thought it showed a lack of understanding about the South.

To South Carolina's Richard W. Riley, the remark was significant more because it demonstrated what he saw as poor judgment on Reagan's part. "The general feeling is that when Reagan gets off the script, you don't know whether he'll go off on cloud nine," said Riley.

"The question is who's going to write the script for the president. Whoever writes the script is the president. I think he's seen as more of a performer than capable of performance."

Even Reagan supporters here acknowledged that the Republican candidate's widely publicized gaffes, which have caused Reagan staffers to cut their boss's public appearances and limit him to his printed text, are eroding his support. Virginia Gov. John N. Dalton, a Republican who speaks optimisticly about Reagan in his state, stresses that Reagan will have to work hard if he is to win.

"The thing that he's going to win on is to talk about national defense, talk about inflation, talk about unemployment, and talk about how we solve the problems of America instead of spending his time talking about the Ku Klux Klan or China or the kinds of things that don't really deal with the major problems facing America," Dalton said.