I got the impression that naruto was the 7th and actually pretty recent in the office. So it would make no sense that he was to back off from the job in such a short time.

Maybe it is some kind of translation issue. Maybe Kiba is "badmouthing" Naruto to try to look cool and hook up with the chick. Kiba had this kind of rivalry with Naruto over Hokage position. Or maybe he isnt talking about droping the job but some kind of political posture, tradition, idea or something similar.