If you can't motivate your child to push themselves, then I believe you have to push them == eating vegetables
Sorry - I took a little liberty in quoting you. But this is how I remind our kids (and myself) whenever I'm making them do something that they would avoid if left to their own devices.
I remember an analogy from Tony Robbins in a talk about personal growth: In weightlifting, if you're doing a set of 10 repetitions... which repetition is most important? Which stimulates the most growth? #9? #10? No -- Number 11.