My dd is 27 mths and if I suggest, or start to pick up her toys in front of her she gets upset, demanding that I don't touch them. It is a stage she is going thru (she put them there and she doesn't like for me to move what she has done, and she also doesn't want to put them in the toy box herself).
I am not sweating it. If I ever catch her putting toys in the toy box (usually it is just incidentally), I praise her, but I do not insist or even suggest she helps, in fact, I wait until she is asleep or out of the room to pick up most of her toys!
However, I do insist on her throwing away her trash or food she is done eating. She is pretty good at this, and she also knows to stay in the kitchen with open-top cups and not to dump food and drinks.
I think 2 or before is a good age to start instilling things like keeping their toys picked up and them taking responsibility for their things (toys, drinks, etc.), but don't stress if your kid is not going for it. I think that gentle encouragement is ok on the picking the toys up, but no forcing the issue on a 2 yr old.