This happens to me a lot more that I would like it to, especially when we have special services and the guest soloist/choirs don't bring their own musician. Sometimes I get frustrated when I can't catch the song that they are singing, but that's when I decided that I would learn more songs. Not just that, but being proficient in chord progression and scales, that would make it a little easier.
But most of the time, I don't play, because I don't want to mess up the sound of the song.