How long does a discharge take? (repost & is this text true)

I've made the mistake of joining the military chasing a bonus. Long story short, a girl said it wouldn't workout essentially because I'm broke. So the next day I was talking to the Natty Guard (it was the first office I thought of) and I swore in last month. Problem is now I realized I made an emotional decision and I actually want to go Marines. My recruiter got annoyed when I told him i'd like to discharge and said I'm not a priority for him so it'll take up to a year. ps: I haven't gone to bet or a drill yet