I would like to propose the following badge:
This would be given to the users whose question gets 15* up-votes before receiving the first answer.
EDIT: An alternativ to this could be that the badge is won if the users receives X number of up-votes before he receives an answer that is up-voted Y number of times. Thanks @belisarius for the comment!
The last may avoid childish behavior, since otherwise it would be in basically everyone's hand to avoid you getting that badge, a quick nonsense answer could spoil it for you too.
I think I would be a good prize for, a clearly good question asker with a (community judged) hard to answer but very interesting question.
The disadvantages (I can see) is that it maybe it will encourage difficult questions (as opposite to good ones - since hard can be good). I don't think this would be a serious issue since basically it will encourage people to make up-votable questions rather that un-answerable ones.
That said, in my opinion, it is still think it will be a nice price for a an apparently great question in a very particular situation due to the normal speed of responses.
Keep in mind that everything from the name of the badge, the amount of up-votes, if it's bronze/silver/gold is just a suggestion by a very imagination-wise limited human being, everything is completely open to suggestion.
So, what do you think?
*I would have suggested 10 but then every time you won this one, you would have won the nice question too, maybe 10 points is almos impossible and badge should be gold or maybe it should be 5 votes, up to you.
Pushing it a bit harder, a "Impossible Question" (silver/gold) could be a follow up to this badge, with say 25 up-votes.