Some rabbits can be sensitive to too many veggies, or a particular veggie, but it just depends on the rabbit and what veggies are being fed. A sign of problems would be mushy runny poop, or signs of discomfort from gas.
If you change a rabbits pellets or veggies, it should be done gradually to avoid digestive upset. New foods should always be introduced one at a time, starting with small amounts, and gradually increasing over at least a week. It is usually fine to just give grass hay immediately, as it rarely will cause any digestive upset. Any good grass hay is fine(timothy, Bermuda, orchard, meadow, coastal). Grain hays like oat, should have seed heads removed, and even then some rabbits can be sensitive to it.
If you reduce the veggie amount at all, then you will want to keep an eye on your buns water levels to ensure that he is drinking water as you reduce the fluids he is getting from veggies.
http://rabbit.org/faq-diet/
Depending on where you are located, what you are able to feed your bun may be somewhat dependent on that factor. You may not be able to get the type of hay that some of us normally feed our rabbits. Yellow hay is fine for fiber and roughage, but won't have many nutrients in it, so you would need to also make sure your bun was getting enough pellets/veggies to supply that and keep him at a healthy weight.