My three and a half year old has a very limited number of vegetables that she will eat. She started to get much pickier with food between ages 2 and 3. You can't shove the food down their throats, and I think it is a big mistake to turn eating into a power struggle - I think it ultimately does more harm than good when it comes to instilling healthy eating behaviors in a child. So I think the most important thing to do is to keep offering veggies and eat them yourself to model the behavior. It will probably be a long haul (as my own kiddo is demonstrating), but I think the long term goal is to communicate that veggies aren't going anywhere, they are always going to be part of the family diet. My hope is that, in the long-run, if I don't make a big, nasty deal about it now, then my kiddo will come around when she is more grown-up and more mature. As long as your doctor is comfortable with your child's nutrition, I think that staying the course, however long it may be, is the best thing you can do.
Best wishes,
H. S