I think your girlfriend wins this one, though I believe the matters is slightly more complicated than others suggest.
Basically, because Spring 2008 is part of a new calendar year and is not immediately upon us it is the most natural one to refer to as "next spring"
_____________
EXPLANATION
Some people insist on a nice, simple rule that tells you exactly what to say in any given situation. But that is to treat language as if it were all cut-and-dried, its terms all precisely defined, rather like mathematics or logic.
Now language should not be IL-logical (or perhaps better anti- or contra-logical), but it is not all about logic.
Now the word "next" is not an absolutely precise term. There may be ambiguous situations and differences in regional or personal uses. But MOST uses should be fairly clear. And when they are not, there are usually slight adaptations or additions you can use to MAKE your meaning clear.
Do note that in the expressions "next spring" and "THE next spring" (mentioned in another answer) the word "next" does not function in exactly the same way. The two are not interchangeable. (For one thing, "THE next" is precise in a way that simple "next" is not.)
__________
As a rule of thumb, "next" in "next spring"or "next Thursday" (or "next week", "next month" or "next year") does refer to the first upcoming season, day, etc. that fits. (Example: it is now Saturday, Nov 24. If I refer to "next Thursday" that means Nov 29. That should be quite clear.)
BUT it begins to become a bit more complicated, esp. when you get closer to the upcoming day, etc. That's partly because "next" then comes into conflict with other terms.
a) we also refer to the CLOSEST one as "THIS" (Thursday, spring, etc). (Note - "this" and "next" may be very distinct, but are not ALWAYS so nicely and neatly divided.)
So, in the Thursday example -- if it is only a day or two past, I would tend to use "THIS Thursday" to refer to the one just past, and "NEXT Thursday" to refer to the one coming up.
BUT, if I'm saying the same thing next Tuesday, I would naturally refer to Nov 29 as "THIS Thursday", and as a result, most likely shift "NEXT Thursday" to Dec 6. (Of course, as I've been suggesting that the two terms do not simply and equally divide the matter there are situations where "this" and "next" might be used to refer to exactly the same thing.)
b) when we refer to days, which we specify as part of particular WEEK, or when we refer to seasons, which we specify as part of a particular YEAR. And again, we bump into the "this" and "next" issue.
For example, going back to the Thursday thing -- I am currently in THIS week, so I tend to think of "THIS Thursday" as the one contained in this week" even after it is past, and "next Thursday" as the one contained in the week following the current one.
(Observe that the slight modification to "this PAST Thursday" may help to resolve any ambiguity for the listener. Also, observe how the same issues arise with the terms "this" and "last".)
Yet again, when you are only a day or two away "next" does not work so well. (If something is tomorrow, I do NOT say "NEXT Sunday", etc. If it is yesterday I do not say "last Friday", "last Saturday" etc. regardless of week divisions, etc)
__________________
Taking all this into account
Spring of 2008 is indeed the next spring to arrive it is not immediately upon us, AND it is not part of the current (calendar) YEAR. By all these measures, it ought to be "next spring". "THIS spring" would more naturally refer to the one just past, since it is included in THIS calendar year (which you might also call "last spring", but again, beware of the ambiguity).