Just pulled up the pictures from our DL trip to check (we took a picture on every ride the first day). Mom (32yo) and DD (7yo) went on 24 attractions. This accounts for things like a trip on the Monorail as 1 ride, and the Train as 1 ride, and the trip to and from the Island as 1 ride... As well as seeing Captain EO, It's Tough To Be A Bug, climbing the tree house, and such.
I don't think we "hurried" at all. We got there around 9:30 or 10am on a Sunday (so, not at rope drop). I heard everyone tends to head to the right, so we went to the left, and started with the Jungle Cruise and Indiana Jones first. We hit multiple things at DLR and DCA, because DD BEGGED for The Little Mermaid to be her first ride--but we compromised, and made it a first day ride instead of the very first ride.
I didn't take pictures of it, but it sure seems like we did the Tiki Room that first day, too, because I *needed* to stop for a Dole Whip
We didn't do any sit-down meals that first day. We did the free breakfast at the hotel, hot dogs for lunch, and ... I can't remember what we did for dinner. I think corn dogs maybe? LOL... At any rate, we weren't eating enough to feel like a beached whale, so we didn't really take much time out from riding and doing things
Oh, and this was during "ski week" (Feb 26-March 3), so it was "off season" but kids were still out of school in the area. (Stupid ski week!)