Cruises are taken offline I think 3 days prior to embarkation to set the manifest. It can still be booked at that point but one must call. However I don't believe they offer any special pricing within that close timeframe.
The "last minute" specials are the "guaranteed with restrictions" offers, often referred to as *GT (IGT, OGT, VGT). These can appear at any time but usually within the PIF period (so ~90-120 days out). There also are sometimes FL Resident specials and military specials that come out within the PIF period.