Tucked under the bleachers of the Orange Bowl, wedged between the aisles of Catholic churches, stuffed into migrant sugar cane camps and piled into National Guard armories, the new Cuban refugees have southern Florida bursting at the seams.

"We are now in a crisis situation," said Tony Ojeda, refugee coordinator for Dade County. "We're reaching the physical point where we can't hold any more of these people in south Florida."

More than 18,000 have sailed to Key West in the last two weeks and 14,000 of them have ended up in the Miami area. Of these, more than 7,000 have been released to relatives in the Miami area. The others are still being fed, clothed and housed by the government in Florida while waiting to fill out forms and be permanently resettled.

Meanwhile, refugees are flowing into Key West at the rate of 2,000 a day, twice as fast as federal officials, working around the clock, can process them and refugee organizations can transport them to permanent homes.

President Carter's announcement today that the federal government would help pick up the tab for refugee assistance -- which has been costing Dade County more than $50,000 a day -- was welcomed here. But local groups said that the federal disaster officials are not moving quickly enough to cope with the logical crisis posed by such a large influx of destitutes, non-English-speaking refugees.

"It is absolutely enaotic," said Donald Hohl, associate director of the U.S. Catholic Conference, which has volunteered to resettle 65 percent of the refugees. "We're in an uncontrolled situation. It's like a mammoth monster, a lumbering giant on its own course."

No one was prepared for the size of the rapid influx, Hohl said, "so we have had extreme difficulty moving people through the system.Officials are loading refugees in Key West and bringing them to the Miami processing center when there is no capacity here.

"Even after we process them, we have to put them in holding centers while we locate sponsors. By the time the sponsor gets here to pick up a refugee, we can't find [the refugee] anymore. There's no control at the gate. Refugees are walking into the community on their own."

Hohl partly blamed the federal government for "changing horses in mid-stream." When the Department of Health, Education and Welfare (now Health and Human Services) abruptly decided last Thursday that the new refugees did not qualify for transportation aid under the existing Cuban refugee program, the Catholic Conference and other volunteer groups pulled out of the resettlement effort.

Sunday, the State Department agreed to travel reimbursement, but not to travel advances, so it took two days to set up a credit system with the airlines, Hohl said.

Federal disaster coordinator Thomas Casey, who arrived this week to take over the operation, was optimistic, however. "When HEW severed the umbilical cord, it took time to get started again," he said. "We have control now, but the system is overloaded . . . the system is flexible enough to expand."

Federal officials announced today that refugees are eligible for food stamps. A federal processing center at Opa Locka Airport will replace the Dade County center at Tamiami Park. Three Nike missile sites near Miami will receive refugees from Key West, and a tent city at Eglin Air Force Base, near Fort Walton Beach, is being expanded to receive more Cubans.

The Florida National Guard, which has deployed 1,050 troops to transport, guard and feed the refugees, sent an additional 300 guardsmen to Key West today to quell disorderly conduct among 4,000 refugees crammed into a Navy hangar there.

"Key West is going to sink into the ocean if we don't get those people out of there," said National Guard Col. Jack Beaver. The guard has asked the U.S. Army to take over.

Ojeda is relieved that the federal government finally is stepping in. "Our system is grinding to a halt. Our volunteers can't sustain the pressure. The pace at which the federal government has responded to this enormous problem has been incredibly slow."