if they don't let people leave to prevent total state collapse then they're starving their own people (by means of the american trade embargo); if they do let people leave, it's to tighten their stranglehold on the country.
The single biggest problem would be rebuilding the US manufacturing base. Once that happens, the US would be fine. America's probably capable of autarky: it's got the natural resources, population size, and technology.
The US didn't impose the condition of being a resource-poor island on Cuba, nor did it impose the condition of economic mismanagement on it (apparently so bad even the Soviets complained about it). The US imposed the condition of a trade embargo, and that's it.