[I]t’s not exactly that Obama influenced black opinions, would be my guess. It’s that African American voters who really don’t care very much one way or another about the marriage issue — but do consider themselves on Team Democrat — are now aware that marriage equality is the normal position of that team. Or, perhaps, that those who think of themselves (implicitly or explicitly) as Team Black now have a revised view of what that team’s position is. Or, perhaps, people who are on Team Church and Team Democrat now realize that those two are in conflict and they have to choose, while before they were getting only one signal.
John Sides insists that presidents generally can't move public opinion:
Obama’s potential leadership in this case doesn’t suggest presidents have broad persuasive powers. If Obama’s endorsement of same-sex marriage did shift the views of some African-Americans, that is still a shift among only a minority of a minority of voters in, as far as we know, a single state.
Scott Lemieux agrees:
[A]ssuming arguendo that Obama’s position-taking has in fact increased support among African-Americans — this represents a fairly unusual political situation, in which 1) a stalwart part of the Democratic base 2) among which Obama is particularly popular has 3) a position that is in tension with much of the rest of the rest of the Democratic coalition 4) on a relatively low-priority issue for most voters 5) on which public opinion has been trending positively (including among African-Americans) anyway. It’s not like this kind of dramatic shift can be replicated in all that many other cases.
Adam Serwer adds:
Another factor here is that I think opposition to same-sex marriage among black Americans is wide, but for the most part not particularly deep. This is why black legislators who support same-sex marriage don't get punished at the polls.
Micah Cohen is wary of over-interpreting the poll:
First, polling has tended to overestimate support for same-sex marriage ballot referendums by about seven percentage points. In addition, the sample sizes for demographic subgroups like African-Americans are small, producing large margins of error. Moreover, voters who are newly converted to a candidate or cause may support only tenuously at first and may be persuaded to revert to their prior position.
Everyone got over their optimism now? Good.