Yeah, try some simple stuff first. One option is to sort of just talk over the chords instead of singing for now. Heck, some songs are based on this approach anyway. That's pretty much how I play and sing Lou Reed's "Walk on the Wild Side." Just talk those lyrics over C-F and then do your best with the doo-doo-doo-doo-doo parts. One problem I have is that I tend to strum to the beat of the lyrics, instead of strumming to a more regular beat. I think this "talking blues" thing helps with that.

DC