How we cite our quotes: All quotations are from Harry Potter and the Half-Blood Prince.
Quote #7
DUMBLEDORE: Draco, you are no assassin.
DRACO: How do you know what I am? I've done things that would shock you.
DUMBLEDORE: Oh, like cursing Katie Bell and hoping that in return she'd bear a cursed necklace to me? Like replacing a bottle of mead with one laced with poison? Forgive me, Draco, I cannot help feeling these actions are so weak that your heart can't really have been in them.
DRACO: He trusts me. I was chosen.
[…]
DUMBLEDORE: Draco, years ago, I knew a boy who made all the wrong choices. Please let me help you.
DRACO: I don't want your help. Don't you understand? I have to do this. I have to kill you. Or he's going to kill me.
Okay, so the truth comes out: more than feeling special because Voldemort singled him out for a mission, Draco is terrified that if he fails, the Dark Lord will kill him. So, yeah, he's not really feeling like he has a lot of choice in the matter.
But as far as the choices he is making go: his attempts to kill Dumbledore have been pretty ineffectual to date, to the point where even Dumbledore wonders if Draco is failing on purpose (or, at least, choosing not to try very hard).