Part of the reason Republicans want less immigration is that they expect immigrants, once they become citizens, to vote for Democrats. That is also, in the view of many Republicans, part of the reason Democrats want more immigration.
Venezuelan immigrants are fleeing a failed socialist state. So were the Cuban immigrants to Florida.
Presidential Vote: Florida
I admit that my view of the subject may be biased by the fact that the only Venezuelan refugee I know personally is a libertarian activist living in Chile and doing her best to prevent it from turning into another Venezuela.