A few years ago, I was at a cabin with a friend outside of Santa Fe.  We go for a hike, nothing crazy, relatively flat compared to the steep mountainsides, but it was at 8000'.
I was huffing and puffing something fierce.  I'm totally out of shape, I get it, but my heart wasn't beating fast or anything.  It was purely a breathing thing, which was weird to me.  I don't think I'd ever been that out of breath without my heart pumping fast from running or whatever.
I just had to go slow, and I was fine.  Elevation is a sonofabitch.