Sporting events trigger this gut feeling for me. The most recent one I can think of was when Meb won the Boston Marathon. This is, of course, kind of silly since I don't know the man and have nothing to do with his accomplishments, but I certainly felt a swell of pride when he won and when he spoke about what it meant to him. The Olympics trigger this feeling as well.
The other times are other things of personal significance to me that also relate to national achievement. Scientific achievements in particular, as I feel part of both the American Tribe and the Science Tribe.
In any case, it was a stupid thing for a First Lady to say.
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I think you're both underestimating how much people hated Nancy Reagan. I can't quite recall if Hillary was more loathed by her opposition while she was First Lady, but she was certainly pretty hated.
Of course, the winner by a mile in this contest is Rachel Jackson. I recommend some reading on the 1828 election for background. It's one thing for dipshits on Facebook to talk shit about Michelle Obama, but the disrespect to Jackson from actual politicians is pretty unrivaled.