Is there a limit to # of AAA packages that Disney will sell?

[ADisneyQueen]

I'm pretty sure that there is a limit to the # of AAA discounted room onlys at each hotel for each date(anyone know differently?). Are there limits to the number of AAA packages for each hotel? Should I be in a hurry to book my mid March trip? I have airfare, but can't make up my mind about which resort to pick.