Actually, when I teach an absolute beginner I start with ONE chord songs. It may be hard to believe, but you can actually play some songs that we normally play with two or three chords with just one chord. The two I've been using are "Old Blue" and "Swing Low"
The first time you do it, it sounds a little strange, but it really does work. This allows a beginning guitar player to get used to one chord and the idea of strumming on each beat. They don't have to worry about when to change or what the next chord is going to be. It works great.
Once they have the idea of that, you can add a second chord to the same song. They already know the song, so then they can start concentrating on what the two different chords are and when the chord changes happen.
If I'm teaching using Swing Low, I will introduce the third chord after they are comfortable with the two chord version. "Old Blue" we just leave with two chords.
I'm sure there are other songs that work with one chord -- I'd be curious if other people have tried this and what other songs work!