It's probably just the added 'pressure' of playing along with something or someone. Try watching the video and tapping along with the rhythm for a few times, then try playing.

I'd suggest trying to play along a couple of times, then go onto the next lesson; you can always come back to this on the next day and try it again.

I've only known of one guitar player with no sense of timing/rhythm, and he couldn't distinguish between 4/4 and 3/4 timing.

Just stick at it. You'll get it eventually.