Yes, it's possible that the "bully pulpit" of Presidency can change public opinion to some degree, though there is statistical analysis out there that largely discounts the idea. It certainly it's possible for public opinion to be at least nudged in one direction or another by the power of Presidential persuasion, but in the case that everyone's talking about today, I think it's really pretty simple:
When you're out of a job and running out of money, the domestic lives of homosexuals is probably not of singular importance to you.
When you've lost your health insurance and are facing expensive surgery, the liberal War on Religious Liberty® doesn't occupy much of your time.
When you're on the verge of being evicted from your foreclosed home and are facing the prospect of having to live out of your car, you're probably not thinking about the looming threat of shariah law. Except maybe for the ban on usury.
When you look at it that way, the shift in public attitudes on gay marriage is not hard to explain at all.
Either way, because bread and butter generally take electoral priority over homos and abortionists, it's probably a good thing for Democrats to keep encouraging Republicans to prattle on about these bullshit cultural issues since, in the long run, it only makes them seem silly---irrelevant at best, punitive at worst. On the other hand, it would be nice for Democrats to make some more concerted efforts to, oh I dunno, be a little more proactive in pushing for legislation that would help those same Americans actually get the jobs, and money, and mortgage relief they want, and health insurance coverage that they can afford, and maybe prison time for the people who looted their 401(k)s. Heck, it might even give the voters another reason or two to pull the lever for Team Democrat come November. Just a thought.
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Vitelius