Happy to get bitten or not, Jack hasn't, actually, been thinking of it as a fight to the death. He's so used to playful brawling with Spike (as with John before him) that it really hasn't sunk in that he's fighting a killer of Slayers, and that Spike's playing this for real.
Even when Spike manages to dodge in past the sword and starts to rain blows on him, he's still laughing fiercely, high on adrenaline, each impact creating shockwaves that thrum through his body until he feels like he's tingling all over with it.
It's not until he goes down and realises how fierce Spike looks, his earlier grin exchanged for intent concentration, that he starts to get a different sort of tingle, the first pricklings of real fear. Spike's stronger and faster than he expected and, while he's still got the sword in his hand, he's kind of reluctant to try and use it in the only way that would actually have any real effect on Spike - beheading.
"Kind of feel like we've been here before!" he pants out, trying to make a joke of it, even while he's trying to wriggle out from under once more, slashing awkwardly with the sword to see if Spike will try to protect his precious coat, even in a dream.