As John Sides notes, while there is as of yet essentially no evidence of a net national shift in public opinion on same-sex marriage since Obama came out in favor of it, there is at least some evidence tentatively suggesting that Obama’s announcement has increased support for SSM among African-Americans. I endorse John’s bottom line:
Because Obama is still very popular among African-Americans and because his shift on same-sex marriage was publicized widely, some blacks could plausibly take a cue from him and change their positions. Maybe, as Jon suggests, many of them didn’t actually have strong opinions to begin with. But Obama could still have been the catalyst for their own shifts in opinion.
Two caveats, however. First, it would be nice to have more polls to back this up. Second, 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.
To the last point, I would add that — assuming 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.
Second, I would note that one effect of position-taking by prominent public officials is that it tends to sort public opinion among partisan lines. Health care reform became more popular among Democrats but less popular among Republicans as the debate continued, for example. I would not expect same-sex marriage to become significantly more popular overall in the short term, but I would expect it to become more popular among Democrats (and relatively less popular among Republicans). This would certainly be consistent with increased support among African-Americans, suggesting that the limited data isn’t just a mirage. While this effect of presidential position-taking is real, however, the political utility of these effects in most cases is very limited (although as Adam says for this particular case in blue states with relatively large African-American populations holding referenda on SSM it might well matter.) If the president could transform public opinion by making his positions substantially more popular among the public as a whole (rather than making public opinion on individual issues bear a greater resemblance to the existing broader political coalitions), this would be more useful and important. But there’s no evidence that this power exists in most cases, and at least as of now Obama and SSM has not been shown to be an exception to the rule.