Slate had a similar article on a simliar survey just a couple of weeks ago. This survey showed that
feminist women were less happy than women who didn't subscribe to feminist beliefs. There is a lot of analysis in this survey of those results though, and some interesting ideas put forward.
First the numbers conclusion (not the why): Across the board, progressive women are less likely to feel content, whether they are working or at home, and no matter how much they are making.
Possible reasons:
Conservative argument: Feminism is undermining marriage, and making it difficult for women to be married and happy.
Liberal argument: Reality hasn't caught up to feminist ideals.
The main argument that the author the article presents is that the more options you have, the less satisfied you will be with what you choose. More traditionalist women feel that they have defined roles, and are happy with those roles. They argue that more feminist women have many more opportunities available to them, so they are less likely to be satisfied with whatever they choose. Clear expectations made for happier people.
This tends to agree with the proposal that IJ put forth, though with a subtle twist. My interpretation of IJ's idea is "unhappy people become democrats because they want to change things to make them happier." A generalization, but correct me if I'm wrong, IJ. This seems to propose that people who want to change things become democrats, and this makes them unhappy. They become unhappy because they have higher expectations and are thus more dissatisfied with what they have.
I don't know if any of this is true (measuring happiness is not very quantitative) but it is an idea to toss around.