As I have explained elsewhere, one of the most difficult obstacles for beginners to overcome is the ability to sing a melody in rhythm while playing a strumming pattern. Even after the ability to change chords smoothly has been achieved, the particular coordination required to sing and play may remain elusive for the student.
Of course, repeated study and practice of the rhythm course contained in "The Path" is essential to overcoming this obstacle, and I want to give you some more resources and approaches for dealing with this.
As explained in "The Path", it is the syncopation required by most melodies that makes them especially difficult to coordinate with the strumming. That is why I suggest simplifying the melody, and removing the syncopation first, learning how to sing along without placing notes on the upbeat, but placing them on the downbeats instead.
Of course, this will make the melody sound more "stilted", but it will get you moving in the right direction, and you will be much more able to put it all together, and do the song with syncopation after mastering it without.
Here is an example of "Eleanor Rigby" with syncopation. Listen to the midi. The chords are playing on each downbeat, which is how you first learn it, that is, with a straight quarter note downstrum.

Now, listen to the midi for the following version, where the melody notes are placed all "on the beat".....
We have moved the word "all" to the downbeat of beat 1, measure 2, instead of the upbeat of beat 4, measure 1. We have moved all other syncopated notes to the nearest downbeat. As you can see, it sounds "stiffer". Make sure, however, that you can do it this way before you try it with syncopation. If you need to, take whole song and sing all syllables on downbeats.
To transition to being able to sing with the syncopation while playing, first do the singing without playing. Do only two or four measures at a time, over and over. Do it with the foot tapping as in all other exercises in the rhythm course. Focus on the syllable being spoken AS the foot is up. You may be tempted to stop your foot motion... don't!

Let's find out what to do after we have gotten comfortable playing without syncopation. How do we transition to playing WITH syncopation?