OK, to start - different companies have different fiscal planning cycles. What I suspect he's saying is that he really won't know 6 days into the new year. The first Monday after New Year's is generally one were half the office is sick, several important things are broken, and everyone is trying to remember what work was on their plate before the holidays. It's not a day where most managers are ready to think about long term planning or budgets for people they can't hire for several months.
It's good to keep in contact, but you want to watch the frequency of contact. Once a month or so is fine, more will get obnoxious. To skip the New Year recovery period, I'd advise waiting until mid-January to give the office time to get rolling again, and then send a quick, politely worded mail.
Given that the manager has told you that he may not know much until March, if you don't hear back from this, let it go until late Feb/early March before you write again. If you haven't heard by April, give up.
In the meantime, the promise of a potential job offer is not a job offer - keep looking. If the job isn't in the budget yet, there's no guarantees here.