“People won’t vote based on the unemployment rate, they’re going to vote based on: ‘How do I feel about my own situation? Do I believe the president makes decisions based on me and my family?’”
He's right, of course, though for 9.2% of those people - not including those who are not in the official "labor force" - that "own situation" can be described as "unemployed".
I don't understand why his statement was controversial, nor why he thinks this is a fantastic distinction to be making. Maybe he thinks the BLS numbers overstate how bad things are. I see more commentary from people who think they understate how bad things are, as the unemployed have generally been unemployed longer than usual. I'm not sure how labor force participation compares to its usual rate when the headline unemployment number is 9.2%.
The thing about that longer duration of unemployment is that it means -- a bit glibly -- that 9.2% of Americans are really getting it in the balls, whereas if the unemployment rate were 8% but with higher turnover some multiple of that would be getting it, perhaps, just hard enough not to vote for the President's reelection. So I could imagine how, in a one-man-one-vote scenario, the current situation would be better for the President than 9.2% would suggest.
It happens to be the case, though, that voters do vote based on their perceptions of how others are doing, not just on how they themselves are doing. If he was asserting the opposite of this -- which, insofar as what he's saying can be interpreted to have content, I believe is the most plausible interpretation -- then he is, in fact, wrong, at least according to the best evidence of modern political science academics.