In Nichijou, characters sometimes make this kind of face when something frustrating or very stupid happens:
Is this a reference to some other popular animated character, or is it a unique way of expressing an emotion in Nichijou?
I think it's just Nichijou's art style and how it expresses the fact the characters are gone past surprise at strange happenings and have come to accept it, the glazed over eyes and straight-line emotionless mouth indicate this quite well.
In cases where it's something stupid, it gives the impression that the characters can't even justify a response, because the joke or suggestion was just so stupid that it's not even worth the effort. So they give blank expressions and try to move the conversations on. This is usually accompanied by an awkward silence. This is common outside of anime as a 'tumbleweed moment'
I'm pretty sure that it isn't a reference to any other animated characters and is just Nichijou doing its own thing :)