You are trying to do 2 things at once. For it to work, one of them has to become automatic. The easiest thing to make automatic is the guitar part since it is machanical in nature. Think about driving a car and all of the things you do automatically. You can hold a conversation, or sing, while driving.

So like Haghj500 says, work on making your guitar playing automatic.

I can't sing, so I don't have this problem :-). I admire those that can sing and play though!

Try to trick yourself. I played Blackbird for some people at work...sort of a spontaneous thing. As I was playing, somebody asked me a question. It wasn't until after I was done playing that I realized I repsonded and kept playing...and didn't miss a beat. Normally if somebody talks to me I have to stop playing to respond. I'll bet if I started thinking about it at the time, the wheels would have fallen off!

Perhaps you could trick yourself humming like compart1 suggests and as that feels good, strart bringing the words in.

Just some more ideas and insight. Hope some of that helps.