This is the only way i can play guitar...play and sing at the same time.... I started learning specifically to do this..... well some things i can point out are... as others have said it before....get the rhythm into ur brain ...u shud be able to hear the song mentally and make out the strumming... and when singing.... don't pay attention to the chords...they shud switch naturally. The key thing to do this successfully according to me is ....u have to simply fall in love with a song ... so much that u want to play it right no matter what....that's what happened for me...
Also, the key is to work on small chunks say a line at a time or max a paragraph. Work on it till you are comfortable.
I was facing the same problem (Singing during playing guitar) But then I ralize that singing is not my job and i've had to choose one thing so I chose to play guitar. I think I can do a better job if I concentrate on just 1 thing.
zombie by cranberries another cool song to sing and play ironic by alanis morrisette, head over heels, your oughta know, you learn, hand in my pocket all cool songs to sing and play.. some are pure girl songs due to lyrics some r uni*** but cool sing and play songs all of them.