You've already gotten plenty of really good advice. I just wanted to add that I have the same problem but not all songs. Some songs I can do it (sing and play that is ) but some are a bit more difficult.
Just keep practicing (and practicing

Bob
Thank you both. What I need is a better metronome.
I am going to try this: While on the two-mile hike with the dogs, I will put in an earplug and strum on my ol' fat belly as if it were a guitar. At least my left hand and arm will be in training.
Does my guitar sound really bad? I mean, if Neil were playing it, would the sound be bad? Do I need to dig up a fruit jar?
Sam