This question gets asked a lot over on the photography board. There are a lot of variables that go towards answering this question. What kind of camera you have (more specifically how many megapixels it has), what your picture taking habits are, what kind of resolution you use to name a few.
If you can fit approx 2200 on a 2 gig card, then I'm guessing that you have about a 3.1MP camera and are using the highest setting. Thats pretty good. It gives you about 300 or so pics per day.
2 Trips ago I filled a 512mg and 128mg card on my 3.1MP digital P&S camera and also took 4 rolls of film with my film SLR camera. Last trip (no kids and I made it a photography based trip) I had upgraded to a 6MP digital SLR and in 4 days took just under 1500 pics. I had 3 1 gig cards, fill all 3 then downloaded 1 to the laptop and filled it again. I got on average 330 pic's per card.
Taking a laptop and downloading to it daily is an option. Using the CD burner service at the parks is another option if you get in a pinch near the end of your trip. On a topic in the photography board, someone posted this cool toy, used in conjuction with a laptop hard drive:
http://www.geeks.com/details.asp?invtid=A-DPM1&cpc=SCH .
Or another option to make sure you have enough memory is to buy more memory. Prices have come and are continuing to come down considerably in recent months. Buy.com has GREAT prices (especially for SD cards). I just picked up a SanDisk 2 gig SD card at Office Depot for $45. In my opinion, you can never have enough memory, especially for vacation and most especially for Disney.