Recommendation Letter Request: No response
I am not in your field. But from a faculty's perspective, the lack of response does not necessarily entail that the professor is unwilling to write a recommendation letter for you. A faculty's life is much busier than you think (this is something I did not know/agree when I was still young and crazy); it is possible that the professor forgot to get back to you and/or that s/he is currently out of touch. If I were you, I would wait for a day or two and would send a polite email telling the professor that you decide to seek for help from from another person due to time constraint (and this is exactly what you need to do in order to ensure that the universities you are applying to receive all of your application materials on time and to give another person sufficient time to work on your recommendation letter).