For now, at least, he doesn't do more than shift to make use of more of the room she's offered. While there probably is good reason to suspect that he might need to rest at least more than he's used to needing to, neither does he actually want to do so. Not when it would mean admitting that he's not as invulnerable as he likes to pretend to be and never mind that she's one of the few people who's well aware of the fact. And can probably see straight through him even now, for all that this has never been enough to get him to actually change his habits any.

(To say nothing of the fact that it is still a point of familiarity, and that's something that he's more than willing to cling to, given the situation as it currently stands.)

Fortunately, he's saved from actually having to answer her question about the possibility of him needing rest by her sudden outbreak of coughing. And sure, he's aware that she's most likely well aware that he's avoiding the question at hand, but just at the moment he doesn't particularly care either. He'll rest later; for now there's her well-being to see to, especially given that he knows full well that she'd have still been trying to work if she hadn't been ordered to bed.

"You're sure there isn't anything I can get you?"