It's the latter. Chase thinks they should look at an aspirin overdose, considering Hannah's known history of taking too many pills and the fact that she's a young woman, and, therefore, crazy in the head. Chase thinks he's really earned House's love now, but House just snaps that Hannah's taking sleeping pills has nothing to do with her mental state. You lose again, Chase. Foreman walks in, and House snaps at him for not being at Hannah's bedside to keep her awake. Foreman says that doesn't matter anymore, since Hannah's liver function tests just came back, and they're "through the sky." Which kind of sounds like he's saying that Hannah's liver is functioning awesomely, but it really means that her liver is dead. Hannah will need a transplant in the next six hours or she'll die, and the Evil Transplant Committee isn't about to give a liver out to someone with an undiagnosed illness that will just kill it again. Then again, the Evil Transplant Committee doesn't like to give its precious organs out to anyone, does it? Foreman says that the only option is to test Hannah for whatever conditions can be tested for in six hours. Since there aren't any, they're out of options.
But House won't give up! Hannah and Max have the same blood type, which means they could be an organ match. If Max gives up part of her liver to Hannah, that will buy them some time to save Hannah's life. It's perfect, except for one thing: Cameron is in the room, and she doesn't think it's right for someone to risk her life and give part of her vital organ to someone who's about to dump her ass. House admits that this is tacky, but that won't stop him from making it happen.
House goes into Hannah's room ready to do his very best acting performance. He introduces himself to the ladies and gravely informs the now-orange-colored Hannah that her liver is a dier. Hannah doesn't have much to say about that, since she's half out of her mind from not sleeping. But Max's reaction is exactly what House was banking on: after hearing that Hannah is ineligible for a liver transplant, Max volunteers her own. House acts like that idea never occurred to him. Max tearfully begs him to let her do it, saying that she doesn't care about the risks to herself. Max and House both turn to Hannah, who's keeping herself entertained by doing her impression of a zombie. "You're very lucky to have such a devoted partner," House tells her pointedly. Hannah continues to stare and look extremely scary. House, on the other hand, looks like he might well be feeling just a little bit guilty about the situation himself.