TA few weeks ago, the Jimmy Carter campaign in Florida printed and mailed out 11,000 fundraising-event invitations bearing the name of Gerald Lewis, the state comptroller, as one of the major sponsors.

On Sept. 10, too late to do anything about the invitations, Lewis announced that he was defecting to become chairman of Florida's draft-Kennedy organization.

That in itself was a minor embarrassment. The fundraiser Thursday night, featuring Rosalynn Carter, was a great success, and her two-day swing through the state took in $250,000.

Beneath the six figures, however, just three weeks before the first critical test against Sen. Edward M. Kennedy [the Democratic Party straw-vote caucuses], problems are emerging. And if there are problems here -- in a state regarded by Carter supporters as a bastion of strength for the president -- it is said that there will be worse problems everywhere else. Items:

Two of Carter's chief money-raisers in the state, Raleigh Green and Arthur Courshon, say that they are increasingly finding their traditional Democratic targets "soft," in Courshon's words.

"I wouldn't be candid if I said they were enthusiastic," said Green. "I don't see the kind of enthusiasm I see for [Republican contender] John Connally. A lot of my traditional Democratic contributors are going for Connally."

Carter's Florida campaign direc- A1 tor, Jay Hakes, says he has been finding a "lackadaisical" attitude among Carter supporters toward the Oct. 13 caucuses, where their presence is essential in the race against the draft-Kennedy movement.

According to campaign sources, a dry run at summoning cadres out for Carter was tried for Mrs. Carter's airport arrival in Orlando Thursday and was, for the most part, a failure. The White House advance team had to drum up a crowd instead.

Most of Carter's Florida supporters say they will remain supportive. But in interviews, many display an increasingly defensive posture and, at times, a sense of isolation and frustration that gives a downbeat and tentative cast to their support.

Here are some responses to a question about whether Carter has been an effective president:

"He's been as good a president as we've had since before Nixon," says Allan E. Keen, a real estate and investment broker who ran Carter's Seminole County campaign in 1976. "The big disappointment has been inflation and I don't think anyone could have done much with it."

"I'm satisfied generally with the job Carter is doing as president," said Richard Pallott, a banker who just contributed $1,000.

"He may have a job that's impossibly hard," says Fran Pignone, who coordinated the Orlando event for the campaign. "I think he is trying to do a creditable, honest job."

"There are times for all kinds of presidents," said Orange County Democratic chairman and prominent Carter supporter Tensi Shirley."There was a time for an LBJ. I don't think if we had a Jimmy Carter up there then we could have gotten all those programs through. After that, and after Nixon we needed someone like Jimmy Carter, someone who was anti-establishment. I think they put too much faith in the man. They thought he was going to abe able to perform miracles."

Courshon, a Miami lawyer who serves on Carter's national finance committee, had this to say: "I still think he can do the job, but he's going to have to focus on the problems. I think he's going to do it. But I just don't know."

Among many nominal Carter supporters, said Courshon, "I sense a desire to see him do the job and a desire not to walk away from him. It's like a team that's hired a good coach and they really want him to win the game."

Even the most ardent Carter advocates in the state -- the ones who came to know the Carter family intimately in 1976 -- recognize the president's problem nationally and in the polls and have difficulty concealing the pain and resentment it causes.

"The people believe in Jimmy Carter and think the rest of you guys are the problem," declares Richard Swann, one of the earliest and most active Carterites in 1976. "They believe that at the time he begins to campaign and brings his message directly to the people, it'll be an entirely different thing."