Hotels tend to be packed during the famed Dinah Shore Weekend held in Palm Springs March 29 through April 2, 2017, so book as soon as you can. It's usually a good idea to reserve your room well before the end of the previous year, and as early as a full year before the big weekend. However, it is possible to score rooms in Palm Springs and the surrounding area even at the last minute, albeit not likely at the official host hotel, which is the Hilton Hotel. Keep in mind also that this is the very same week of the highly popular LPGA golf tournament that inspired Dinah Shore Week, the ANA Inspiration Golf Championship.
You can get a full list of host as well as sanctioned partner hotels at the Club Skirts hotel page. This year's hosts, at which many events are taking place, are the swish and sexy Palm Springs Hilton Hotel and Spa,the chic Hard Rock Hotel Palm Springs, and the more reasonably priced Courtyard Marriott.
If the above packages have already sold out, or you're looking to stay at a different property in town, keep in mind that the Palm Springs Bureau of Tourism has an excellent GLBT Travel and Planning site, and I also have an article on this site describing about some of the best GLBT-friendly accommodations in Palm Springs.