1
general::
Phrase(s): by the day
one day at a time. • I don’t know when I’ll have to leave town, so I rent this room by the day.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Also, by the hour or week or month or year. According to a specific time period, as in I'm renting this car by the day, or He's being paid by the hour. This usage generally describes some kind of rate. [1400s]
American Heritage Idioms