You're crossing over from naive, to stupid.
Florida is one of the States with the highest number of illegal aliens in the nation, and what border do we share?
Alabama?
Georgia?
But we do get tons of boat loads of illegal aliens brought in by smugglers from Haiti, Cuba, The Dominican Republic, Jamaica...
The tidal shorelines of the US, our off-shore islands and cays, are American soil, and Cuban rafters use them to gain entry, as do Haitians, Dominicans, etc.
Shut down the SW border, and the coyotes go sea bound.
We have problems stopping tons of cocaine and pot coming in yearly, and you think that the Coast Guard will be able to handle the drug smugglers, AND the coyotes?
The solution is to eliminate the problem, the most logical one is to document temporary workers. It worked before, it will work again.
The root of the problem is in Mexico. Send the illegals back and let them find a solution.