Reply #102: Easy: it wins votes from centrists who are worried the Obama is too far left.

[Donald Ian Rankin]

When Obama and his supporters are rude to left-wing Democrats, they're actually talking for the ears of centrist floating voters.

You pretty much answer your own question when you say "Centrist Dems are the ones who will stay home in November". I'm not a mind reader, but I think it's a fairly safe guess that what motivates Obama is the calculation that most left-wingers will vote no matter what he says, whereas appealing to centrists will lead to people who would not otherwise vote voting.