Let me just say that I have not read any of the previous posts before typing up my answer. I rarely do.
I suppose there could be a number of different meanings in that line. You're right, it is hardcore and they way in which Sarah Michelle Gellar portrays it is very, very serious. Almost in an Edward/Bella kind of way but less whiny, which is nice. It's just very...passionate I think. I don't know.
The line could be taken in a negative or a positive way. As I said before, she says it with so much passion but passion can be negative and positive right?
If you want to take it in a positive way, she's tell him her innermost thoughts. How she feels when she kisses him. Saying that you want to die could be a positive thing in some ways because it's saying she feels that strongly for him. However, writing this now I decide that it's very unlikely that the line was said for positive reasons. It was more likely said for reasons to hurt him.
So, negative. The line was most likely said out of spite towards him. Aiming to hurt him in a way that just saying any old thing couldn't achieve. I think maybe, though, there could also be a hint of shame. Again, she is telling him her innermost thoughts in order to hurt him just a little but she's also saying that she can't really believe that she is betraying her duties as a Slayer by falling in love with a Vampire.
I'm not sure, just my thoughts.