The longest trip we've taken Kiwi on was the 4+ hour drive home when we first got him. He pretty much just slept or played with the little toy in his travel cage the whole way. We did stop about 2 hours in to give him some water/food, but a longer drive didn't phase him at all. In fact, he LOVES the short car rides we frequently take him on now.
We personally travel with him in a small cage (about 18x18") with a single perch, 2 removable dishes and a toy rather than a carrier. He seems to like holding the bars with one foot for balance when stopping and making turns, and I would be scared he would flop around in a smooth sided carrier. He also enjoys having a toy, which you can't really hang in a carrier. A few years ago we were evacuated for a fire, and he spent 2 days in his travel cage and didn't seem to be bothered by the temporarily small accommodations. He will be spending around 4 days in it on the road when my husband and I move this summer, and I just can't see how that short of a time is going to affect him in any way (especially since we will be making stops every few hours to give him food/water and letting him out at the hotels). For parrots who are fine with car rides, I think a few day drive isn't going to leave a lasting affect. I will say, some parrots are absolutely scared poopless of driving in the car, regardless of what you transport them in. If your bird is one of the ones who is scared of car drives, I highly recommend you start now taking him for short drives around the block to get him use to the idea before you subject him to a few day long trip of terror.