The month first format. Do you, as an American, find this unnatural?
And: If you were in a hurry, would you start typing the month first (as this is most natural for you)?
Edit: This question differs from this one because I'm asking how likely you would enter mm-dd-yyy in a dd-mm-yyyy input if you were in a hurry (even if it was labelled). The other question is about appearance rather than entry. A nuance, yes, but this is UX and it is not a nuance in this context.