Thanks to Ellis for his thoughtful post. I essentially agree with all of it. I was not trying to make the case that the PM's popularity doesn't matter, but only to show that it is not obvious that the PM's shijiritsu is always the most important factor in electoral outcomes.

The only thing I would quibble about a bit is Mori: he really was an exceptionally unpopular PM from day one.
According to TV Asahi, his highest rating was his first, 33.9% support versus 37.8% opposition in May 2000. From there things deteriorated sharply: 17.3% and 22.2% support rates, versus 68.4% and 64.2% opposition rates in June 2000. In short, I would argue that Mori really is a clear case of a very unpopular PM leading his party into a general election. Of course, specific factors, DPJ weakness, a sympathy vote for Obuchi (??), etc., might limit the implications we can draw from this case, but this is a clear case nonetheless.

That said, I would also add the caveat that the shijiritsu does not necessarily only reflect the PM's personal popularity. After all, the standard question does not ask respondents if they support the Koizumi or Noda PM, but whether they support the Koizumi or Noda cabinet. The follow-up to that question gives respondents a chance to indicate whether their support or non-support has to do with the quality of the PM or other reasons.

Best,

Paul