I was at Disney June 23 to July 3 this year, and I was really nervous because I thought that it would be really crowded being the week before the 4th. But I didnt think that it was all that bad. Yeah there were alotta people, but you have to expect that because it is Disney!
As for booking a room, we were there for 10 nights, origianlly at Port Orleans Riverside, but then we were moved, and we were given like 5 other choices, and this was probably 2 months before, so for them to give us so many different choices, it couldnt have been that booked up. We ended up at Animal Kingdom Lodge.
In 2002 I went the week after the 4th, (July 6-14) and the crowds weren't all that bad then either.
But I have never experienced Disney on the actual 4th. BUt i wanted to stay because they did Sorcersy in the sky at MGM! but leading up to the 4th I didnt think that it was all that bad!
Hope that helps!