I second what Jeff says. If you allow yourself to feel the music, you will, I think, begin to sense when it's time for a chord change because what you're singing (or what the singer is singing or the notes that perhaps the lead guitar is playing) won't sound right without a chord change.

What's more, with more experience, you will likely be able to sense not just when to change, but which chord to change to, even if you haven't heard the song before.

It will happen. This also relates to the nerves suggestion that several of us posted above. Nerves keep us from being in touch with our intuition and the groove of the song.

Hope that helps!