Are you too tense? How about a little flow and just start strumming and tapping your foot, easing in with humming first, then trying some singing? Who cares if your singing is out of key or anything. Just get in the swing of it and then hit the right notes when you've got the flow of things.

Anything worth learning isn't going to happen right now. So practice, practice, practice, and relax. Let it flow. Start with really simple stuff. I posted a reply to a thread on this topic and I started out with "Chasing Cars" by Snow Patrol. Just simple down strumming, and you can even start just speaking the words, then make your way up to singing, then singing it properly. It worked for me and I'm hopeless, I can assure you. :D