Again, he left out "just" in front of "concerned." That is the gaffe.
We all know there are poor people who have no desire to be anything but poor. That's always going to be the case. Then there are people who have fallen down and want to get back up. Obviously those who have fallen into the ranks of the poor want to get out, and those are the type of people Romney is most concerned about.
I doubt it was just a "just" deletion. The entire comment would have been restructured if what he was saying is the range of his concern is more pandemic, and thus, he feels the need to have policies that focus on the middle class to go along with those that will lift all boats. It makes no sense to say I am just not only concerned for the poor, but my focus is going to be on the middle class because the poor are getting plenty of food stamps and such.
The comment has this connotation, that hey, the poor are getting plenty of help from the food stamp president, and the president is screwing the middle class, and so that is where I am really needed - as a champion of the hard pressed middle class. Somehow I suspect that is Mitt's instinctual reaction.
I appreciate per your putting up the whole comment, that Mitt later says the poor have it tough too, but the entire message is rather delicate, and needs to be structured so that bits of it cannot be cut off and used, particularly when they are so poorly phrased.
Much clearer, and politically safer to say, would be to say, yes, the poor need help. They need better schools, better opportunities, and so forth, but the middle class needs help too, and they are not getting it. See how much better that sounds? It is not hard really. It really isn't.