Prior to 1965 we as a nation agreed that this type of low unemployment was good. After 1965 we don't have that agreement as a nation. We haven't matched the low unemployment rates that we used to enjoy either since before 1965. If you look at long-term charts of the unemployment rate, it is really very dramatic. Simply throw out the 1930's and you'll see that prior to 1965 our unemployment rate was on average a solid 25%-30% lower than after 1965.
It is no accident. Republican economists, including Alan Greenspan and others, have been quoted as saying that they have to keep unemployment up over 6% to keep lots of willing workers for big corps. Big corps don't produce jobs, so it doesn't make sense that the republicans would think this way, but they do.