The United States Government has shown differing levels of support for each of the governments that have controlled Cuba. Today, the US opposes the Cuban Government and favors anti-Castro exiles.
In the early days of Cuban democracy, the political party of the Cuban President was often that of the current US President.
Tomás Estrada Palma was strongly supported by Roosevelt, who was disappointed at his resignation. This almost led to fighting in Cuba, but the United States stopped it with another occupation.
After that, the United States supported the Conservative Party, even though it won elections by fraudulent means. In 1916, the US endorsed Menocal, sending him weapons to maintain order, and helped him crush the Liberal revolution.
The United States had mixed feelings towards Machado. When he became dictator, some Americans wanted to condemn his corruption and prevention of democracy. However, American business interests in Cuba prevented this.
When Ramón Grau became President, the US was worried. He had refused to accept the Platt Amendment, but soon proved to be corrupt and friendly with US business interests.
The US Mafia was primarily responsible for Batista's return to power. During his reign, tourism and US investment boomed. The US was highly supportive of him since its companies prospered in Cuba.
During the struggle against Batista, the US constantly supplied his government with military equipment. At one point, the US also assisted Castro, but evidence of this happening is still classified.
After Batista fell, Fidel Castro took power. The large numbers of Communists in the Cuban Government made the US Government unfriendly towards Cuba from the beginning. Eventually many other events resulted in the current situation of almost no relations, economic or diplomatic, between the two countries.
Hopefully, the future will change the relations between these two countries. Today, the United States basically refuses to recognize the Cuban government until Cuba will accept a capitalist system.
Imagine if Cuba refused to deal with the US until the United States became Communist. The United States would find this absurd; perhaps it will realize that its policy is no different.
If the current Cuban government falls, it is highly doubtful an another anti-US government will be able to take power. Should those who once supported Batista take power, relations will probably improve dramatically overnight.