Not a big thing, B.B. King says he can't play and sing at the same time, he has done pretty good for a few years too.
I think it is mainly a thing of practice. If you are thinking about chords, chord shapes, strumming, melody and lyrics you are on overload.
Multi-tasking can be a good thing, but it can be difficult. As the others have said practice. When learning a new song start with chord progression, get it under your fingers and in your ears. Then hum the melody and work on your timing and strum. When you have chords and strumming on auto-pilot try adding the lyrics.
For me I need to play a song at least 150 times before I am close to learning it. I also believe it is easier to play a song when you don't need to read it from the sheet.