Haciendo una búsqueda en Google estoy de acuerdo contigo porque me salen resultados como: "I was stalled and the days were clicking by toward my contracted deadline"
"There was no way I could back out of this corner and the days were clicking by"
"As the days were clicking by we knew that it might be the only way to get the client out quickly"
"The days were clicking by—three of them already—and he could feel his body changing"
Parece que sí que se refiere a que los días pasaban rápido o, como se suele decir, pasaban volando.