AF - I have to nag my (considerably younger) DD to do her homework and get moans and rolled eyes etc. But the difference is I know she is v motivated. She wants to go to Oxbridge, as I did, or do Fashion at St Martin's, depending on her mood. She's v competitive and wants to be the best. So reminding her of her long term goals helps to motivate her to work even when she doesn't want to (she's naturally fairly lazy; or maybe more fairly, she likes to follow her own star and not be pinned down by what her school dictates she should do that day). She's also always done well academically so wants to live up to her own and others' high expectations.
What you do if you have a kid with low/no expectations and without a habit of success? I'm not sure. I suppose you start by believing in them, even when they don't believe in themselves - I think that is probably the main reason my dd has done well so far; high expectations. I remember teaching her to read and her saying over and over that she 'couldn't' read this or that and my saying 'yes you can, I know you can', and she could. Maybe that was easy for me because I've always been an academic high achiever so transferred those expectations onto her. Maybe you need to up your self-belief and belief in her?
When I look at the 16-18 year olds I teach, all I see is enormous, amazing potential. They can do so much, achieve so much. The world is their oyster, even if they don't know it. I'm determined to get them through their easy peasy qualifications because frankly it will take so little effort on their part, but might be the difference between making the shortlist or not, getting that first step on the ladder, in the fairly near future. I do believe in all of them, even though (because? 
) I don't know them at all.
Obviously, it's easier with other people's kids because there is none of the personal, deep-rooted angst and confrontation that you get between children and their own parents. But you obviously care, deeply. So you just need to find a way to transfer that caring into something your dd understands as positive rather than something your dd reads as nagging or pressure.
FWIW, if it was my dd I'd be sitting her down and asking her exactly where she saw herself next year/in a few years/in her ideal world etc. And then encouraging her to look at exactly what was her preferred route of getting there. At her age, she should be positive, inspired, excited about what she can do.
Unfortunately, at that age, many teenagers (I was one) have no idea of this - the world seems scary and unknown and harsh. She is at the perfect age - every possibility is open, no doors have closed. She should be drunk on the excitement of that position, not on alcopops or cheap cider. It took me until my 30s before I realised that - wish I'd understood that earlier. So I do try to get that message across to my dc.
Sorry - rather lengthy and a bit full of 'I's'. 