A PhD program recommendation fell through. How do I deal with this? I am finishing up a MA in Global Affairs, and I am in the process of applying to several doctoral programs. Two and a half weeks ago, I asked three of my professors if they would recommend me. I made sure to note in my emails to them that if they chose to support me, one of the program deadlines was substantially sooner than the others. Two responded positively almost immediately, but one did not. However, he has encouraged me on numerous occasions to apply, and speaks very highly of me. Needless to say, I was very surprised when he responded 5 days before the first deadline to say that he was not prepared to recommend me. He said that he normally only write recommendations for students who have served as his GA, and that if I want him to write one for me I have to draft the letter I expect him to write. I said I could do that... but would we be able to do this in time for the upcoming deadline? He said no, and there was no way I could ask someone else with such short notice.

However, I really do not know what I should say to the other people who recommended me. I know they have already submitted their letters. Do I say that I simply couldn't get my act together in time, and risk looking unprepared? Do I tell them that one of my recommendations fell through, and look like I must have done something to change that person's mind? Do I tell the full story, and look like I am just trying to place blame elsewhere? Or, do I just not tell them at all? They all know each other, so they could find out even if I don't say anything. None of the options seems great, and I am kind of at a loss. 

Edit to add (taken from comment): My main concern is that asking someone else to submit something last minute or late might not be appropriate.
Get another letter. Grad app deadlines are many times not as strict for letters as they are for your application materials.