I wouldn't say, eat it or go hungry. I read a great book, called " Child of Mine: Feeding with Love and Good Sense", by Ellyn Satter. My 2 boys, ages 2 and 4 are not picky. They love veggies, tomatoes, fruit, etc.
The author does suggest that you eat together as a family most of the time for dinner. Make your regular meal, not a special one each night. Serve your dinner family style, and bring the dishes to the table so they can help themselves. Say you are having chicken breasts, green beans, and red potatoes, salad, and bread. The author says most kids will eat bread, so they won't go hungry. Always offer something the entire family enjoys. You can even put a bowl of fresh fruit on the table. The author often does this, even if it's a bowl of canned peaches. So for a couple of weeks, they may only eat fruit, bread, and chicken, but if you repeatedly put veggies on the table every night, eventually they will try them and like them. I always put veggies on my kids plates, whether they eat them that night, or just have a couple bites does not bother me. I never force, I never talk about it.
I never fed my kids the "baby" way. I rarely make nuggets or mac and cheese. My kids eat their sandwiches and hamburgers with lettuce and tomato. They eat whatever I make, and generally are not picky. I am not saying they are perfect eaters. I just wanted to start them out right nutritionally, and not have eating problems like I have.
The book is great and has an entire section devoted to preschoolers.
Lori