I've read "The End of Science Fiction" and I heartily recommend it for how it portrays different people's reactions to an imminent end.
A brilliant film describing the same thing is the Canadian
"Last Night". It made me think a lot when I first saw it. Find it and watch it if you can, it's worth it.
I'm sure I would not face many moral dilemmas in such a scenario. My morality is my own, not the law's, and I would never hurt another human being (or animal, personally that is, because I do eat meat), even if they were to die anyway five minutes later. I'm not even sure if it can be called morality or maybe ...squeamishness. Say someone was suffering, and asking me to end it, I still wouldn't. But anyway, that's a completely different discussion.
I would get rid of my boring day-to-day affairs, like dsvick, like paying bills or going to work. If I had taken on something voluntarily though, I might still finish it, if I thought the person that was waiting for it still cared. I guess responsibility fades away as slowly as morality.
What it comes down to, I think, is why you do things. Do your actions lose their meaning when there is no future? Or is it irrelevant?
What I would find a real problem, is who to spend the last day with. We all have loved ones scattered everywhere. Parents, lovers, children, friends. And each of them have their own network of loved ones. How to combine them? Who to see and who to ignore? Who to say a proper goodbye to?
Oddly enough, when I watched Last Night I did not feel panic, or hopelessness, I felt relief... To have it all simultaneously end for everyone rids us of all the anxiety - both the everyday kind, and the fear and loneliness of death. Very strange feeling.
Okay, this was a more serious post than I intended
I'll stop now!
(Edit) Oh, morality that is imposed rather than internal I would get rid of. I might go out naked, for instance. I might also try dangerous things, as I wouldn't have much to risk. Dangerous to myself, that is. Drugs, really extreme sports, I don't know. There's so much freedom when there's no future.