Speaking on that subject- I find it difficult, if not impossible to do so for some (actually many) songs due to the brain multi-tasking issue.
Gail Ann Dorsey recommended starting off really slow with a metronome until you can sing with facility. Other advice I got from a musician was to start off with just the root notes and gradually fill in as you get accustomed to doing two different things at the same time-
Thoughts? Other suggestions?
I realize that for some people, it comes naturally, even some drummers like Don Henley and Roger Taylor could sing and play at the same time. But Frank Zappa once stated that he could not -