I don't know if you call that sufficient back-up for the claim of women being their "core constituency" - certainly there are constituencies, such as African-Americans, where Democrats consistently do much better still. With women, they don't even always attain a majority - in a presidential election, if the Republican candidate gets half of the female vote or very close to half, it's game over because it'll surely mean he/she also has well over half of the male vote.