I agree that Obama's policies are no question better for the poor. It just strikes me that that happens via rhetoric that mostly talks about the benefits to the middle class. Policy is less often pursued "in the name of" helping the poor.
Perhaps it has something to do with the whole "individualistic" streak in American national consciousness? I've heard people say that in the US, everyone thinks that where you are is where you got yourself - poor people are poor because they are lazy, and so on.
This plays a huge part. The narrative on the right is that the rich got rich solely by their own talent and skill, and that the poor are poor because they are lazy. Of course there are qualifications made, but this is the underlying theme. Obama made a point that rich business people actually utilize a lot of public infrastructure and got where they are through collaboration. That led to a new line of attack and outrage that one could suggest that the rich didn't build their business themselves on the part of Republicans.