It isn't easy playing and singing at the same time.....I've found over the years either the guitar playing gets simplified a little, especially if it's a slightly complicated strumming pattern, or the voice tends to be weaker because I'm concentrating so much on the chords. However......we are not alone in this. Take a listen to, say, some Cream....studio versions of songs feature some amazing bass lines by Jack Bruce, and some great vocals.....but listen to some of the same songs live, and you'll notice the bass lines are very much simpler....and the vocals aren't as strong. If such a high-class musician (and I'd rate him in the all-time top 5 (rock) bass players) can't reproduce live what he does in the studio, what hope is there for us mere mortals?
My own way of tackling a song I want to sing and play is simple....I learn the guitar part I'm playing till it's second nature and I can almost do it in my sleep - or at least on autopilot! - then start singing along. It might take me a while, a fair bit of practice, and a whole lot of frustration - but I'll get there eventually, because I'm (a) motivated - I wouldn't be playing the song if I didn't like it and (b) I'm too stubborn to admit failure....I've come so far the last few years, I'm not going to be beaten by a song I love, and (c) did I mention I'm stubborn? Single-minded is more like it...once I've decided to learn a new song, I'll concentrate on that almost exclusively till I've got it down to my satisfaction. Stubborn, single-minded, tunnel vision, totally focussed....that's how I am when I'm learning a new song.
Works for me, anyway - others may have different methods of learning a song.
Oh and some songs are just impossible to play and sing anyway....Sweet Jane springs immediately to mind. Unless, of course, you're Lou Reed. I'm still struggling with that one, been trying to get the riff and vocals in sync for about 5 years now. Pfft. Gave it up as a bad job....I'm NOT Lou Reed!
"Sometimes the beauty of music can help us all find strength to deal with all the curves life can throw us." (D. Hodge.)