The men clasped hands in victory Wednesday night as they emerged from a detention center.
"This shows that in this country there is democracy and that justice still prevails," said Raul Sosa, 36, a tow truck company owner who had waited hours in the rain outside the center.
The swim has prompted the Coast Guard to investigate its own behavior, and the case has caught the White House's attention, reports CBS News White House Correspondent Bill Plante.
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Administration officials believe the six Cuban men paid professional smugglers to drop them off near the Florida coast, something the officials say is a growing problem. Two of the men made it to the beach, while four others were picked up a few yards out to sea after being blasted by a water hose. One swimmer was doused with pepper spray.
Under existing policy, foreigners who reach U.S. shores are allowed to seek asylum, while those intercepted at sea are generally kept out of the United States. The Coast Guard's vigorous defense, part of which was seen on local television, outraged many and set off demonstrations in the Cuban-American community.
PROTESTS IN THE STREETS
Up to 3,000 people gathered at the Coast Guard's Miami Beach station, blocking the main access road between trendy South Beach and downtown Miami.
Demonstrators held signs saying "U.S. Coast Guard: Pigs Like Castro" and waved Cuban flags as they sang the Cuban national anthem. In Hialeah, the police chief needed stitches after he was hit in the head with a rock and the mayor was shown on camera grabbing a man and punching him several times.
The refugee flow from Cuba has increased dramatically over the past year. The Coast Guard has picked up 932 people at sea since Jan. 1, almost as many as in all of 1998. Cuba watchers warn that the island's desperate economic situation could lead to an even more serious problem.
"At any moment, the Cuban government can open the floodgates," explains Cuba expert Pamela Faulk. "The U.S. has to worry about when there's an increasing interest in leaving and an increasing number of boat people."
The Coast Guard says it's investigating whether its personnel used excessive force, but Clinton administration officials are defending the tough tactics, saing that immigrants have become more dangerous as they have become more desperate.
Privately, according to Plante, White House officials are saying that if this incident hadn't been on TV, the four men picked up at sea would already be heading back to Cuba.
The men will be allowed to stay with family members while awaiting a ruling on their asylum application.