Why do Republicans in Congress oppose the Obama administration's rapprochement with Cuba?
Cuban American Republicans in Florida have a history of opposing Castro. For example, the family of Senator Marco Rubio considered returning to Cuba after Batista was deposed by Castro but decided that Castro was no better. Traditionally the community has opposed rapprochement and favored Republicans. Republicans reciprocate by opposing rapprochement.
Note that the single Cuban American Democrat in the Senate, Bob Menendez of New Jersey, also opposed rapprochement.
One significant issue is the nationalization of property by the Cuban government. Many first generation immigrants lost property that they would like back. Or at least compensated for the loss. Second generation members of the community often agreed.
This may be changing among younger members of the Cuban American community, who are from third and later generations. They vote more for Democrats like Obama and favor normalization of relations. Presumably this means that they accept the status quo loss of property by their ancestors.