A large majority of Americans supported normalization of relations with Cuba at the start of the year, and now that normalization is proceeding support has increased:

Some of the most notable increases in support for normalization and for ending the embargo have come from conservatives and Republicans. While just 33% of conservative Republicans and 40% of all Republicans favored restoring diplomatic ties in January, those figures have shot up to 52% and 56% respectively. On the embargo, only 40% of conservative Republicans supported ending it as of January, and now 55% favor doing this. There is majority support for ending the embargo from Americans of all political stripes. The pro-embargo dead-ender position championed by Rubio, Bush, et al. is not only unpopular in the country as a whole, but it is now clearly the minority view within their own party and even among those that identify as conservatives. Almost all Republican presidential candidates have tied themselves to defending a policy that even most of their core constituents no longer favor. Far from there being any “backlash” to the policy of normalization, Americans of all backgrounds are even more in favor of restored ties than they were just a few months ago.