Yeah, you can get too much vitamin A. But I think you would have to be taking supplements to get an excessive amount . . . not from eating carrots. Or at least I think you really would have to be turning orange before that would happen (he! he!); though I do seem to recall reading about that happening. But a bag of carrots is not THAT much. Check it out, though.
I don't think you can eat too many carrots but they are a really starchy vegetable. Even Weight Watchers has bumped them up to 1 point per cup from 0 per cup. I think its all in what you like and if you are trying to lose weight.
I'm pretty sure that carrots, like many vegetables, contains beta-carotene. Beta-carotene is converted to Vitamin A in the body depending on how much is needed so you can't overdose on it. But yes too much can turn your skin yellow/orange.
The RDA for vitamin A is 4000 IU, one medium size baby carrot has 1500 IU. So you can figure out how much more about the RDA you are consuming when you eat an entire bag of those carrots.
Does it make any difference? Vit A is stored in the body and yes, you can get too much. Skin turning orange is a good indication you are overloaded.