I think most toddlers do that. My son is 5 and I'm surprised he hasn't turned into a great big old chicken nugget as many of them as he eats. He has just recently started eating steak here and there, and will eat taco's with ground beef. He has just as big of an issue with meat as veggies, so I feel your pain on them being too picky.
It was a battle for a long time...I always hoped someone influential in science would decide ketchup was a veggie, because that was the only item remotely close to a vegetable mine would eat. My brother will often times, if he notices Matthew isn't eating well, challenge my son to take a bite every time he takes a bite. Matthew seems to think it's funny and will do it, and ends up eating more than he generally would.
The doctor told me to just keep offering the veggies, but give a vitamin in the meantime. I always tell him he has to try it; he does not have to like it, doesn't have to eat it, but he does have to at least try.
I don't think you should ever force a kid to eat, "clean their plate" or anything like that. There is food I don't like and won't eat, I wont make him eat stuff he doesn't like. Sure there are kids starving in China, but it can be just as painful to be too full as it is to be starving, or to eat something you find disgusting.
I would use caution on juices, even V8...though they contain servings of veggies and/or fruit, they also have a ton of sugar in them, and other juices are very rarely 100% juice. Juicy juice is the only brand besides Gerber that has 100% juice available, but the sugar content is outrageous. It's no better for her than handing her a Pepsi.
Keep trying to get her to eat veggies,maybe try to make a gmae out of it, but give her a Flinstone vitamin each day to make up the difference, and don't stress over it!