The first mishna in Midos tells us that kohanim stood guard in three places in the Mikdash (leviim stood guard in another 21 locations). This din is derived from our parsha where Aharon and his sons are told to be "shomrim mishmeres hamikdash" (3:38). Torah Temimah explains that some varient of the word "shemira" occurs 3x in the pasuk (shomrim, mishmeres, l'mishmeres) and hence we learn that a kohen guard is needed in three locations.
From the placement in our parsha in the context of the discussion of who camps where and the placement of this din in Midos, it seems that this din is not a chovas hagavra obligation on the kohanim, but rather is part and parcel of how the camp should be arranged and how the Mikdash should be setup and built (see Tiferes Yisrael).
According to most Rishonim the chiyuv of shemira is only at night. Even though the purpose of shemira is to honor the Mikdash -- this is an honor guard, not a guard to catch thieves -- and therefore there should be no difference between day or night, nonetheless, the tzurah of the mitzvah of shemira matches what would be done if the guards were there for protection. A shomer by day when not needed does not have a shem shomer.
The anonymous mifareish on MesTamid is the lone view that holds shemira must be done by day as well, and Achronim have such difficulty with this opinion that some claim it is not really what anyone holds.
I prefer conceptual questions to practical ones, but here is what Rashash on the mishnayos in Midos asks: when Moshe gave this mitzvah, there were only three kohanim in the world -- Aharon and his two sons. If three kohanim were required to do shemira during the day, then who was left to do the avodah?