We've only visited Mickey during spring breaks (DL 2004, WDW 2005). From what I understand, US schools have varying dates for their spring dates -- anywhere from mid-March to end of April, I think.
During spring break 2004, we went to DL 3 days earlier than the beginning of spring break holiday. It was the Wed, Thurs, and Friday before. (We took the kids out of school early.) It was very quiet and nice on Wed and Thurs. On those days, we went on all the rides we wanted to go on, several times over. The crowds got bigger on Friday, and you can imagine quite busy after that. On the Friday and Saturday, we didn't do too many rides, tho it was possible but the wait times were longer. We also watched more shows, strolled DTD, and ate at Goofy's Kitchen and Blue Bayou. By Sunday, when it got really crowded, we were off to San Diego.
I think that it is possible to go during busy peak times. You can just adjust your pace to a slower one. IMHO, if your kids are young and you can take them out of school a few days earlier prior to the actual break, you would be better off. Also, it seems to be cheaper to fly mid-week.