I believe that it will be gone by tomorrow. Although the temperature has not been particularly high, we've had a steady rain throughout the day, and rain is supposed to continue through the night. While I would be surprised to see anything left of that minimal pile in the morning, a part of me wonders if it is just stubborn enough to stick around for a little bit longer.
I don't have any concrete proof, but I believe that this is the latest that we've still had snow on the ground in our yard. I know for a fact that I have had to mow the lawn earlier than this on multiple years. This year, I don't plan on mowing it until after I get back from Kansas City after a third of June is over ("No-Mow May" is easy for me).
Certainly, this little patch of snow will be gone by then.