First, the full speech can be found here. I'll quote what I think is the most relevant section.
There are a lot of wealthy, successful Americans who agree with me -- because they want to give something back. They know they didn’t -- look, if you’ve been successful, you didn’t get there on your own. You didn’t get there on your own. I’m always struck by people who think, well, it must be because I was just so smart. There are a lot of smart people out there. It must be because I worked harder than everybody else. Let me tell you something -- there are a whole bunch of hardworking people out there. (Applause.)
If you were successful, somebody along the line gave you some help. There was a great teacher somewhere in your life. Somebody helped to create this unbelievable American system that we have that allowed you to thrive. Somebody invested in roads and bridges. If you’ve got a business -- you didn’t build that. Somebody else made that happen. The Internet didn’t get invented on its own. Government research created the Internet so that all the companies could make money off the Internet.The point is, is that when we succeed, we succeed because of our individual initiative, but also because we do things together. Somewhere, lurking on the internet, is a humorous list of Men's Rules for Women. One of my favorites on that list is "If we say something that can be interpreted in two different ways, and one of those ways makes you sad or angry, we meant the other one." Anyone who has ever met me knows instantly why I would like this rule. But let's not get off topic - I do have an actual reason for bringing up this obscure bit of internet humor. In any discussion, if someone says something that can be interpreted in different ways, it's best to assume a charitable interpretation of their words. This seems particularly difficult to accomplish when discussing political issues.
But one does not have to be all that charitable to the President to see that the quick meme version of his statement was in no way a reasonable interpretation. The "that" which "you didn't build" is clearly a reference to the internet, roads, and bridges - not businesses. The idea that he believes people deserve no credit for their success just doesn't pass muster. If you can read the whole speech and you come out of it thinking that's what he meant, I can only refer you to this.
When the President gets on the podium and says things like "if you've been successful, you didn't get there on your own...somebody along the line gave you some help," it seems to me that he's bashing his shoulder into an open door. Nobody could have reached any of their accomplishments in a vacuum - we all received support from many sources and benefited from the cooperation of many people. We all know this.
It's more natural to think the other side disagrees with us because they misunderstand very basic points - the Righteous Mind doesn't accept that others might understand these points and still disagree with us on other things. Bear in mind, President Obama wasn't there to give a speech on what we all agree on - he was giving a campaign speech where he was distinguishing what his side believes from what the other side believes. The Righteous Mind of the Right doesn't hear the President making an utterly commonsense point. It believes the president just can't be expressing a view it also shares, and instead thinks "This statement reveals his true beliefs - he thinks nobody deserves credit for their work!" And The Righteous Mind of the Left doesn't hear a statement we all agree on, either. Instead it thinks "He's right! Why do those other people believe we're all atomistic, and why don't they see the value of social cooperation?" This is what politics does to the mind. The statement became controversial precisely because the statement is not controversial.
It's amazing - or disturbing - how often people ascribe motives which are only fit for Saturday morning cartoon villains to people with whom they disagree. For example, libertarians justly complain about how often their views are caricatured. If I had a dollar for every time I've been told that I only hold my views because I hate, or when my antagonist is feeling charitable, merely don't care about, poor people/women/minorities/puppies, I'd have enough money to fund a shamefully decadent weekend in Vegas. When you get people like Paul Krugman saying things like "Today's American right doesn't believe in externalities, or correcting market failures; it believes there are no market failures," you'll see the same thing at work. If Krugman had said "Today's American right is excessively skeptical of government's ability to correct externalities and market failures," he'd be making a statement which could serve as the basis of a reasonable discussion. But rather than set the stage for a productive discussion, we all too often reduce the views of others to a ridiculous straw man and skip the conversation altogether. We're all guilty of this. We all think ours is the Obviously Correct View, and that those who disagree with us must fail to see other things which are also Obviously Correct.
A litmus test to always keep around - if you think "the people on the other side believe X," and X is absurd on the face of it, to the point that one would have to be evil or incredibly incompetent to believe it, that should set off alarm bells that you're projecting a straw man rather than attempting to understand. It could be a false alarm. Evil and incompetent people do exist. And some highly educated people believe clownish things. (I'm looking at you, Noam Chomsky...) But that should never serve as a default explanation.