President Carter turned to ridicule and sarcasm today in his war of words with Ronald Reagan, suggesting that his GOP opponent would have a hard time governing the country because "you can't rely on 3x5 cards" and a teleprompter in the White House.

"I have to admit that my opponent is very good at making speeches," the president said at a "town meeting" at Edison Senior High School here.

"A lot of people say he's better at making speeches than I am, and I guess they're right," he continued. "But when you're in the Oval Office dealing with a crisis, or when you're in an international forum . . . or when you're sitting across the negotiating table with [Soviet] President [Leonid] Brezhnev, trying to guarantee the future of our nation and the peace of the world, you can't rely on 3x5 cards and you can't read a teleprompter." (For what it's worth, Soviet specialists say that Brezhnev relies on written notes and almost never speaks extemporaneously in negotiations.)

Carter ridiculed Reagan for causing confusion over "how many Chinas there would be" and for his recent statement about trees causing air pollution. Laughter and applause filled the high school gymnasium, but for the president and his political strategists this question of what lies behind Reagan's polished oratory is deadly serious.

Their answer, which the Carter campaign is trying to convey to the electorate in numerous ways, is very little. "Reagan is too dumb to be president," is the way one Carter aide bluntly summarizes this underlying campaign theme. It is an accusation that the president has not yet dared make directly, but it is a message he nonetheless usually tries to get across, as he did today.

Carter has deliberately used the "town meeting" format -- in which he answers questions from citizens -- to contrast what he today called his ability to "meet those issues, think on my feet, make proper responses" with Reagan's talents. The Republican nominee, with his well-known use of small index cards outlining his speech text, is an accomplished public speaker.

As it turned out at today's "town meeting," the president could not answer the first question put to him, an inquiry about an obscure change in the Social Security law that he finally had to refer to his domestic policy adviser, Stuart E. Eizenstat, who was standing nearby.

And in response to one of several questions about the influx of Cuban refugees into south Florida, Carter hopelessly confused the refugees with the subject of the previous question, the hostages in Iran.

"Now all the hostages still in settlement camps have been moved out of Florida and into Arkansas," he said at one point during his rambling response to the refugee question.

But when another questioner asked why the government did not guarantee "Christian rights," the president seized on the question to assail Reagan's fundamentalist Christian supporters while continuing his ridicule of his opponent.

"This nation was not founded just on the Christian religion," Carter said. "In our nation now, there are those who are trying to define an acceptable definition of who can serve this country, and to define by law or through political persuasion the definition of a Christian."

But, the president added, "the Bible doesn't say whether there is one or two Chinas, the Bible doesn't say how you balance the federal budget. And the Bible doesn't say what causes pollution . . . . It's never been done before, but certain religious groups are trying to say what the definition of a Christian is. And I know you agree with me that that is wrong, right?"

This state, with its 17 electoral votes, was a bedrock of Carter's southern base in 1976. But the president is in serious political trouble here this year for a number of reasons, not the least of which is the flood of more than 100,000 Cuban refugees into south Florida and the administration's handling of that problem.

The refugee issue erupted shortly after the "town meeting" began when a scattering of boos greeted Carter's statement that the federal government will fully reimburse state and local governments for the cost of caring for the refugees.

"I hear a few boos over here on my left about the Cuban refugees," Carter said. "I presume that your families didn't immigrate to this country. You must be native American Indians. The rest of us have all come here later."

Describing the United States as "a nation of immigrants" and "a nation of refugees," Carter defended his decision not to try forcibly to halt the Cuban refugee boatlift.

"I had a choice to treat them as human beings with a precious life or see their lives lost at sea," he said. "And I did what was right."

The president stopped here at the beginning of a two-day campaign swing through his troubled southern base. He later spoke at a Democratic picnic near Orlando, where the small crowd that greeted him was indicative of his deep political problems in central Florida, before flying to New Orleans for a rally and fund-raising dinner tonight.

Carter will make three campaign stops in Texas, the largest and most critical of the southern states, Wednesday before returning to Washington.