Dave Weigel has a short piece in Slate about how Americans don't hate Cuba the way they used to. He shows this from Gallup:
Here is more context, going back to 1996, and indeed it is gradually becoming more favorable over time. Aside from the xenophobia this graph reveals (Canada, people? Japan?) it does not measure intensity, which I think is much more important in the Cuban case. A very, very small proportion of Americans feel strongly about Cuba; the rest have a generalized sense of disapproval but don't care. Get rid of the embargo? Big deal. The embargo is held in place by a tiny but powerful minority. More from Gallup:
2009 Apr 20-21^
People do not support the embargo, but they also do not feel strongly at all about actively supporting change. They just don't care much, which makes it easier for a minority to keep it in place.
My hunch too is that very few Americans care much one way or the other whether Barack Obama shook Raúl Castro's hand, unless it is to provide more ammunition to already existing strong opinions about whether they like Obama or not. In other words, it's only peripherally about Cuba.